my dear children let's start this to the class and further questions in this class will get it solved In the previous class of Exercise 11.1 If you had completed question till six You guys have not completed the link You will find the complete description in the description Lena and further questions in this class If you get it solved then like the video immediately Do it and share this video as much as possible Share it in your friend circle The wait is over, Udwa is one by one Look at the neck of the question, question! Seven is told find the Point at the normal to the curve x p Ratva equation A is parallel to x axis What is asked of us here? Points it has been asked or it is written find the We told you the point in the previous class The question was if we talk about what is in six I told you that if you are asked for points, Whether it is a question or an example what should be asked then the point is to the curve and By doing this, x has to be written as xv and va as va I want to write with wow, save this in your mind should I save it in the question or If a point is asked in the example, then the curve and then x has to be written as x1 and y as y1 We have to write it like give us this curve here What do we do if we are given √ x1 ps of √ y1 = a is to be written in the root like this and You also get this information be it a question or an example Exercise We are talking about 11.1 on the curve itself work on what to work on You have to focus so much on working on the curve only First of all you have to keep the given curve I have to write it as if I have solved it if yes then write it here the given curve all students write the given curve √ a memorize plus and memorize equal A this curve has to be further written like this because points were asked so what have we taken here xv and vav then the value of xav and that of vav You have to find the value when x and The value of Wav will be known at the same point first write it here and do it r eq plus root of vav equals root a ise equation put it first because it will be used It will be used like it is used in question six okay now we'll rough it out We will do it now here it is said parallel to x axis then parallel if in question If it is written then which condition should you use is A1 If it is written normal here then what It is written normal, this is the condition for tension this is the condition for tent when it is parallel If it is normal then we will tell you hey my ave i a2 this is what you need to change Because if we talk about the slope of the curve As for the tent, you have to get it out of your hands If we talk about normal, we talk about normal If you are finding slope then move up a is written as minus and upon the given slope of tent so that's why the curve You have to change the slope, this is A2 which is the line What we will do with the line for slope Find will always change the slope of the curve I have to do it in normal minus up and in tent and this and here if we talk about the curve I have to take it out from which side I have to take it out from the curve we have to draw it we call it curve and anyway in class 12th Have you revised the exercise? of 6.3 because if it is practised NCERT for class 12th of this exercise what are you talking about who are you talking about If NCERT is okay then there will be no problem Because that is the question you are asking here. You have solved this question, you can see it So those who do Exercise 6.3 belong to the same category You have solved it, that is why I am telling you first you have 6.3 Practice in the playlist You will get complete because it is class 12th We completed maths last year, kids you enjoyed it so that's why you are saying it people have fun If it comes then see brother first we will take out m1 m2 here x x means y We will apply this condition, for normal -1 up m1 = m2 from there the value of x1 or y1 If I find it I will pick it up and put it in it immediately You will get the same point for any other variable This is the calculation, let's do the same now what will you do first bro Differentiable from the curve then Do you know the difference, from here to here What is the meaning of what is written d upd You have to keep both the sides, this side also You have to keep it and keep this line on that side also If she speaks, then obey her words will brother d up d one r a ok d one know ho 1 up 2 √ one is small children know that if Differentiable that you come here, do this also like this but y's again will be y's again here You must have known this in class 12th You Differentiable If it is taken out then 1 upt will go and here the parva you have to write your d one in equals write this 1 upstairs cancel this Tova's own d will make an equal cross into then in ratwa's apon one will come out ok Now the points you have taken are x1 and y1 If we draw the curve in an extension then the x1 y1 point will be I have taken it, it is lying down at that point You have to find the slope, this will be used, see How can I answer the question even if it is written normal? Even if you have to calculate the tangent, you can calculate the slope tangent only. Now I understand that we have to find the slope of the angle Later in the condition we will increase m by -1 Let's repeat it once again Whether the question is written in tense or not If it is written normal then you will get the slope of the angle It has to be taken out, like we write here Slope Off Tange slope of tange at et x1 y1 okay from this point we draw this curve and after doing this it was written that okay so what should we do Let's find the slope of m1 m1 d wa kya d one and here you get x1 y1 have to be written down okay now d wa up d a r look at the sheet, here it is, use it then y put this one y1 and this is xv here But if you put it in minus numeration we will get So we got y so y1 in the denominator I got this x so it becomes x1 okay like this After this you have to take out m1 now m2 from here If you find out, then look at the x axis, then you I have to tell you that I write the equation of line here are the equations of line on the x axis now say the equation of line on the x x va e 0 this is us basic I have already told you the basics the x axis is 0 now from here How to remove it? See if we put it like this write 0 x plus ka 0 0 x p 0 slow for I converted it to zero You can write it any way you want, even in three terms You can break it into two terms Take a break, even if it is in four terms Take it as per your convenience If you convert it then if we talk about slow form if y is m p c then y is equal to two If it is a term then you broke it into two terms we will compare it, look at the comparison on comparing wa equals a ps c and here But write it down and the meaning of gate is I gate my dear children gate means What we find after comparing find the value of a i.e. fit of x Here a is the coefficient of x and the coefficient of x is zero, then convert this to m2 and you will get the value of m2 Because if we use condition here then at I have written it here if I had not used the condition But if we keep A only then we understand that the value of A2 is zero It will come, we will compare it, brother, so many notes Now let us rough it out and tell you further is how to solve this If you do it then my dear children the value of A2 Here we write okay now the condition If you want to use it, it is written parallel here writes are the conditions for parallel to move my m1 i m2 we told you it is written normal so You need to change the slope of the curve, okay? m1 m2 does not change, so keep this in mind Any example in any question If m2 does not change then it is ok and If we keep the value m1 this is what I have minus 1 in its xv equals m2 just calculated the value of zero it will go up And what is minus will become plus If you go then write this one down, memorize it. 1 If you cross this into 0 then rate xv this will be 0 Now let's do squaring both sides here then the value of x1 will be zero We Rough We will do it, let's move forward, take notes till then It takes time to rough it out So this is the value that we got for x1 If you square that side, what will be x1 will go to zero, what will be the value of x1 I have to put it in the equation first We told you that use of equation first Now you already know the equation first so what do you write here Put this value in equation first now you The first equation is to be written as r xv rat vav e R A now we will keep it, put the value here so it is zero The rote will definitely come, the value of the rote is always zero waw equal root a okay so y1 root equal So now you will do squaring on the bow side right? y1 equals a comes square side will root It will be cancelled after this There is a point brother because the value of xv is this and the value of wav is this then hens the point hens the point first you have to keep the value of xv You have to put the value of xv first, understood it first xv then wow it came out note down the point now next We will get the question solved for you I told you to learn to read A to Z, A to Z The child studies A to Z and the concept of the same It is not clear that most Read 4 important questions Read the most important questions from him The concept is not clear like many set top teachers are teaching most most important You can score good marks by studying important things yes but you won't get a job soon from A to Z Learn to read A to Z What is A to Z it happens the concept gets clear then somewhere questions came from this book if you read A to Z, okay, the whole book can you tell me without seeing the whole book if remove the book can you say the whole book if a why would you study 2 to Z instead of reading A to Z concept would have been clear there will be no problem with this question Whether we talk about a question or an example that you people are busy with the most important things lying down yes read that too for most important We have not forbidden you to read that as well, but a We are teaching A to Z, you guys please read See if the concept is clear or not The concept should come from somewhere like if we do something Exercise 11.1 Do it if you have solved two root questions Then you can say it somewhere in this exercise If any question comes from them give it to me brother I will solve it if you ask five questions Someone please give me the answer whether I have solved it or not You get shaken, you get shaken only when you are A to You don't read Z, that's why you move from A to Z What will happen if you read it, you can't even move yes that is why it is said that reading from A to Z Learn and the concept becomes clear Read question five concept is not clear now let's rough it out next Till then you guys will talk about question A what to do, if not like the video all students have done this please like something Students like and do nothing else what should all students do like this as much as possible If more new students want to join ho channel then subscribe the channel what should you do subscribe to the channel and You must press the bell icon because It is for your benefit only, whenever we start a new class Rabbit Fire brings notifications by Toy Now get the question written like this question if we talk about a great The question is, let's see who got it first we will write it down that the normal so that's the normals to the curve to the curve wa [ __ ] equal 4 a x R Tange Eights Are tense to The Curve 27 a inva sc equals 4 in aces minus 2a key hole power 3 Now here we are told that I have to prove what I have to do to prove what do you have to do to prove it is normal to the Do you know the meaning of curve normal, equation of Nermal brother wa minus wav e my own apn e this equation okay this is the curve written next to r Tangent to the curve means normal like equation is this curve that the same The equation of this curve should be tangent to its For this you have to prove it, then repeat it once again Do It is said that normal to the curve means is the equation of normal this curve of normal this is this equation is described here This equation is tangent, this curve will be tangent The length of this curve is called tange if this is equal to this then this is the proof Tax If we prove it, then this equation This curve will be normal as well as tense let me explain it with a diagram like this Do you know the diagram of how to make odd power? Look at it. In this x is the odd power on the variable that has the odd power The diagram is formed on the same axis as the The diagram is drawn on the same axis as the If you get odd power on the variable then odd power x on the positive x axis This will form a parabola, it is called parabola, yes now he said as if This is tension and this is normal what is this if it is normal then this is the equation These equation of this curve parabola parabola that the tension is normal as well for this you have to prove it okay We'll rough it out now let's tell you this How will this one be proved 27 A inva squa equals 4 in x in minus 2a to the whole power 3 first you we have to write down the given curve because we To you Told in the whole exercise my dear If we talk about complete exercise for children then You have to work on the curve only, on the curve only If you want to work, then this is why The Given Curve is for you Have to write down the given So do you know what to say in Hindi? Gave Went curve and identity so we know that the equation Will the previous class be about a line or a curve I have already told you, still I repeat it that if the equation of the curve is if it is then highest power is two or greater than two If the equation of the curve is then the variable If the higher power of or is greater than two then the curve The equation will have the highest power, look at its if there is one its two then t hat or two se If we get greater power then the equation of the curve So this is the equation of the curve we wrote like this After doing that, okay, now what do we need? Points We need points because without points we cannot Can't tell the equation of normality normal ba minus vav e human your a x minus x so this is for us should xv and Once we know the wow, we can calculate the slope from that If you take then the points are not given on this nor If asked, then not asked in Quen You have to use its parameters the equation here will write parametric equation parameter equations which are x i A [ __ ] e 280 these are parametric The equations are also verified as squa and 28 is it or not verify How will it happen if both of these are solved If you solve both of these then it will become If this equation gets made then see, I will get it done By the way, we are talking about class th You are talking about conic section read What is the conic section called? Conic speaking section we call it conic section so you read it There will be four types there, the first Circle Second Parabola Third Ellipse and Fourth Hyperbola So you know the parameters of these four. This thing in conic section in class th you were told was that you know the parametric of four So we have written the Paslik equation here As Let us verify it and show you that it If it is made then let's get it made brother, like a tea take out the value from here and put it here x e a [ __ ] so what do we do Look, find the value of t from here or Upon 2a and what is the whole power here this is what we are verifying what are you doing this verification separately If you are explaining the question separately, we will solve it We will do it but we should know this too Even small kids ask questions Even small kids ask questions I tell him to memorize it, what do I say to him After telling me to memorize it, don't memorize it for verification If you are solving this then a and y are squares Upon me 4a square this is cut in this turn it into cross into then see y sc equals 4a 1 comes see So this is its parametric equation if if it weren't there then it wouldn't have happened This equation does not hold if If it were wrong, it would have been written correctly That is why this equation was made You have to understand this separately Now we got a point from here like Point means the value of x and y Bha A Squad 2 Okay, now you need to find the slope as well. differentiable with respect to x so this means that both sides are d Up dx1 d is to be kept on both sides y of the square 2y and do y again come here 4ax kavan then d wa k apne in dx4 ap me 2y 2 to 4 so d wa k ap I d how much did I get for 2 okay now we need to find the slope Normal is written in the question of normal We told you in the question whether it is normal whether it is written or not You just need to find out the slope angle This attention has to be paid to the slope tension only I have to keep it even if normal is written in the question Even if it is written in tense, we will write it here Tent Slope Off pitch a tent at a [ __ ] 2 Okay, so here we'll write the slope of m. Equal wa k upon mendi x is now point put a squa2 near me brother vallu 2a's Apon me wa hai wa tova's value is this The value of the latter va is the next one If the value of x is 28 then cross it out So how much forest is there above and how much is there below, we know Now let's find out the normality of this equation normal is ok note this much now we will rough it Do are the equations of Keep taking normal notes and also take notes simultaneously stay because a formula was made in math A formula has been created in maths Read fast, understand fast and write fast if you understand Equation of normal equation of normal formula then You know, take the point at a [ __ ] 2 a okay tova minus y manav i myv apna a into me x my xv okay so this is xv and this is wav okay is tova minus 2 ava minus the value of vav I have kept it, now after this you have to keep it or take it out but I have to keep this in mind, this is it So 1 up t is the value of A okay up so This will be the value of myv and the value of xv what is a [ __ ] little solve from here let's do a little bit from here Let's solve it look at the t moving up will go minus will be deducted turn it into minus If you turn it into minus t, you will have to cut it into minus t. a minus minus plus a is to the power two of t one will become another into of power 3 now we'll bring this to this side x or Keep it like this, we will tell you here a The rule will be used if you take it to that side plus 280 and plus 8k this is normal The equation turns out to be this normal equation It has come out and this is what is called normal for this curve If this is the tangent of the normal curve if yes then prove it okay if we I ask you if this is a cubic equation is the cubic equation is a triple power The equation is a cubic equation, so its roots how many are you Went How many routes will there be Tell me Bha how many roots have become of the highest power The more there are, the more routes there will be The original would be three three so if we talk to you Like the whole square of Keva minus Kadi A hole will come in this way, if there are three values What is the meaning of the original value? means if x square minus 2 x or take it here write it like this now tell me how we write it like this x square plus to x and minus to 6 e 0 so this is quadratic so how many of x Values will come out here one will come out one mine means the original meaning is this so that's why Here But there are two values of x because what is the highest power here So two values came out there are three powers here so if we talk about If the value of t is 3 then it will be 3 like this We will get power by doing this as we are differentiable what will come on differential wa k apna dt will come equal to minus xt kav one It will become 2a and here there is three power ahead. Now you can get the value of your DT Why should I keep it zero? I am telling you this now How you will write minus if you take common take it or keep it like this, I will tell you to do it later What ok as we have set the value of upd to zero Why did you keep it because we told you all this I have taught it because it is taught We will keep the value zero and you have to understand As the value of the nut is found, the equation will be like this then if the differential [music] If we take out the value from here, wawa our Will the value of DT turn out to be zero? will come out It turned out to be zero, so we kept zero here This is what you have to understand there is nothing else now Let's rough it out, understand? [music] Now let's rough it out, you guys understand Why did we make the value of our DT zero? It is kept fine Now from here we have to find the value of t and in this Put this equation in first keep it in this after taking out the value is up If you solve it with this then you guys should note this much And we're not going to do it rough because we need this just to bring [music] if so look at So if we bring it to this side, then x minus What will happen 2a x minus 2a okay so x minus of 2 il me 3 at [ __ ] so from here if If we find the value of square then x minus 2a is our in 3 so e x minus of 2a upon in 3 How much will the whole power be now? You have to put value in this equation first have to keep it in put this Value Inn Equation First Putting You First okay what do you guys do just note this because this is what we will use, what about this we will use it wherever it is, keep this much of Wa If equal to va is equal then we will keep x minus of 2a upon 3 whole power 1 upon 2 Enter the value of 2a of the EXP in the inu so if we talk here Value after taking XT Common Keep it or take it later, common among both of you brother t is common take it so exponent of minus 2a You will get it later, no problem if you take it in the beginning then still no one will There is no problem, what is the whole power? okay now here comes the a x of plus mine 2a up me 3a hole power Its cost is how much will its uptime be If you plug in power then you will get 3 upts will go into power and turn the power into 3 upto Now meet these two Look at these two, what do these two have in common? I found this whole thing, it looks very common it's okay so note do it now carry it forward yes this is what we have to solve or we have to make 27 ava squa i 4 x minus 2a key hole power 3 ok let's see whether it will be made or not No so so 2a of x minus okay minus common take and x minus 2a to the whole power 1 2.5A and 3A whole power output is common I have taken it from here x and what did you get from here 2 understand because we took minus and common this bracket is complete took it all I also took the common minus, it became a plus This is going to be a minus because the x here If you have minus u then you should make x minus u because in multiple the power becomes plus that is why we took the minus common and there on x minus of 2a whole 3 up 2 up in 3a key hole power of 3 okay here's what you need to do look what is this equal to will go 1 upto 3 upto on 3a key hole power upt plus x mine 2a key whole power 3 upt upon in 3a power 3 upt Now take the common thing in both of these, you will find the common thing If it is there then take it, we will rough it hey look here you can get common towa equals one my 2a to the whole power 3 its 2 and 3a key hole power 1 upt what common got 1 got the upt common ok why 1 upt and 3 If we write the upt like this, 1 pw upt then 1 upt If it gets common then its power will be saved and From here you will get minus and plus and if you All the common has gone, there is no power here Will there be no power left will survive and this was going on here what was going on and write it down low a was running here because atk was If I had done any rough work then I have to write this, it is going on had understood go cancel it now This is the hole of Tova equals x minus 2a Please keep this in mind in Power 3 Apn 2 Apn that he was here so he was left there, write to him Take the whole power of 3a to be 1 upt and here manav plus up 3 solve how much will you get -2 am 3 from here might up 3 will get so much We'll rough it a bit And the answer sheet is visible in front of you, that much I have to bring tova equals x minus 2a key hole power 3 upt upon 3a key hole power and up to minus cut it and you ok now what to do is squaring both sides do it because we need to make ba square Squaring Bothies side squaring bo side karne karte na Ba square will appear here when we delete it then the square will come here x What will be the hole power of minus 2a because the power below will be cancelled 4 up 9 will be cancelled here Now look down and turn 9th 27 27 into A. This is a match Let's go rough it so 27 ava square is okay and in equal 4x minus 2a to the whole power of 3 now look at me The answer is done, see if it matches then the answer matches So note down what all the kids do take note then you will see 4 into equal I'm getting x to the whole power of 2a, now it's 3. The next question is, Nine gets it done Solve quickly take a quick note Now it is the turn of question nine, no more will you do some friendship with him So we put the question here [music] na question naan put ok so you What should everyone do? Write down the questions. it was said here that so that the Normal at any point at any point of the curve of the curve x k equals a cusp plus kati Saiva K Equal A sign of minus Kos is written further i at A Constant Constant distance from The read its origin first Let us get it solved later, it is said here so that means proving what to prove So what is said here is normal Do you know the meaning of normal? It means the equation of What is normal equation of talking about? Whenever normal is written in the equation will talk about off normal The point is written ahead of the curve, this, this What is parametric? If we talk about it is parametric what is it is parametric Understand this Brother We speak parametrically, meaning we speak equations Let us give a parametric equation, and parametric so you know that its If we take out that UPD one So how is the formula derived I will tell you first let us read the equation of It is normal to use it and remove it Then we have to find the distance from the origin We have to find the distance from that too which is constant To find the constant, first find the equation Do this using parametric equations When you use it, you will know the formula this one It will seem so for normal, so x1 and y1 This is what you have to use this is y this is x and this is y this is the point you I want to use it somewhere you can see it Whether it is a parametric equation or an example do it if we talk about the question If the parametric equation is given then the equation Whether you take out tense or normal That is what we use, by taking points Let's use it, I got your point and I understood it have to take out To find out the slope, look at this formula It becomes parametric when the equation is found This was the formula is this u please take out one, did you understand it? Divide wa into give top and bottom D Divide by x why have you taken this tee i.e why this party because if we talk about X who The value is that which is value the variable that is there in it because that is what they speak Brother, first write the parametrics, the given curve the given curve equal to the given curve x a cos plus k t what is the equal of saati and va a seven and minus cut so here miss there is print what is here it is miss print Get it done here if you have a doctor If it is a book by Vinod Kumar writer then you will miss it It is printed whatever value is there in it Those children who have misprints, need to correct them If you have it then it's okay do it now here we are Will Write Ware t is a parametric is a Parametric Here the value of x and y then it is in the term of t if theta k is in term like here theta theta theta If it were theta, then it would be parametric, then with respect to you differential goes to whatever parameter it happens with respect to that only Differentiable parametric if the equations meet then Here T is parametric, so T is with respect to differentiable after then k t plus k t Saati ok product rule will be applied here because there are two here it will become single so d one's own dt-2425 and what happens to coke - coke in coat joe They start with a minus This is the trick, now we are talking about the difference Here the matter comes to first like this I will keep the honor of the second time it became different we will keep the second as it is and first one is different now see t one This plus of this minus is cut so if the d If we talk about our d then a It has come out that okay now we will talk ending it now You have to keep your DT on both sides So this seven minus cut kas ok so what about ba It will happen that your DT will be there, take it forward what will happen to the sign it will be ok on this If the product is installed then first do it like this why will the second digit be minus It will start with CO and will leave minus first second then second again First, okay, let's simplify it a bit. So what will be the cut minus minus plus t what will happen to saati and minus cos this is plus this minus of got cancelled like here It got cancelled, it happened there, so it happened here Saati A what turned out to be Saati so d wa up Wa is to give the divide of t in and d in a We have to give the divide of t then if the value we I keep it for you and that is your sati and x is the value of your dt a If the A is cut then sign me up what came sign up Keep one thing in mind whenever you are asked an equation go if asked about the tent go or normal then don't write it down, what should I do You have to write that you will not be able to sign up or else kos upon sign de If you give me your sign then you will write the quote If you write like this, we forbid it Experiences that we refuse You don't have to write quote, you don't have to write no If the equation is asked, is it tentative or normal? Apart from this you can do the equation If we were asked anything other than this we would sign up. I should not have written the Kos or the Kos would have been my sign So we write the quote but when the equation Say no only when asked and do not write quotes like this You have to use it in the equation just like this You have understood how to use this, now find the slope So at what point will the slope emerge which is parametric not t from the same t point Removing the Slope if we understand then what will we do with the slope Let's take it out, we'll rough it out then we have given you this Told even if it is written normal in the question Or if Tange is written then you will get Slope Tange that is to be taken out So here we find the slope are the slopes off Tange at that time when wa k up x hota na Slope A K equal wa k upd x and the point here is not written whenever you need a parametric Whether it is an equation question or not, If there is an example, write here what is parametric if theta were to be Here we write if there is t then we have to write t so this is what it means which is dy1 [music] Normally, we use this point a little bit because whenever we talk about equation Whether we talk about a tent or a normal one You have to take this point, take the slope We have to find out t and tell the equation for this From point, we have a little bit in long You will have to write this points then move forward this slope attention I have to keep it to myself because If it is used then we are here will write the equation Off Normal because normal is written here at Write this a k t plus ka t sa t then comma do this and write it down a seventy minus of t to the t We took this point For this use the equation of normal at this point If you want to do it then you know the formula of y minus in baw equals a inu in x minus xv and what happens in normal my up is ok So ba minus vav ki If the value is xv and it is v then A there's gonna put the latter seventy minus t Category okay equals my what is the value of your a sign up in cos you have to write equal to x minus xov this If yes, then use the middle bracket a cuty plus k t Saati it's ok now we have to solve this You have to make an equation and then find the distance We will extract that constant on the basis of the You should do that, so turn it into minus a seventy minus minus plus a If it reaches the top in Kas and Equal then Kas in upon sin x minus a into Take a Saati became so clear now look at this cross into dova saati If you want to cross this one into minus of a cy square t this will happen in this a sa t into k t equals what is written above If you put it into the bracket above, then you get a minus of x will become k t because here the minus is minus minus plus will become a tight [ __ ] t because that is squared become minus minus became plus a sati in cos now look this is of plus and this Also the plus has been cancelled what to do now Putting the terms of x and y close together understand that the term of x has to be kept positive Whether it is positive or negative It has to be written only after the term of x, then after that After C you have to plus C means constant is ok so let's bring it to this side so how th and and this one plus ka wa seventy equal what is in it what is in it equal to it Take it to that side and what is common here I am getting it means I will transfer it If we take it to that side then there will be more what is common in this a is visible If we take it, then cos sqa plus sign squa now this is a formula sign what is squa theta ps cos theta If it doesn't happen then let's keep this much note there Do red fire quickly note down all students So much note Now let me tell you further how it will happen here. solve so x cuti plus ka va sign t x k t Poisson equals a because its value is one, now we Whenever you want to find out the distance Distance needs to be found out at any Talk about the equation Whether we talk about a straight line or a tangent whether we talk about normal or not You can find the distance only by making it equal to zero distance can be found by making it equal to zero if it is there then it has to be brought to this side, this is fixed Whenever we talk about distance, it is equal to zero You have to take distance by doing this much attention so put x times t plus y times t minus a e 0 so at 0 0 take it out there is distance let's take it so what happens if you get a formula One has to keep in mind that if A X P B V P what is ce0 and what is the vapour of atxv If you want to find the distance then Put x in place of y and put y in place of va keep the wav then the kof in the root the square of the coefficient of x then plus wa cuffit's square so this is the formula ok so if you use the same then I have I will put zero here, it will remain zero here Zero will come by zero it is not minus a k upon and we have to take this turn because Distance is never negative So you have to take the mode further and now in the root what do we do by multiplying cuffit by square The square is written as cos which means the sum of x It is cos, right? Square it then after this the plus now comes here But take Ba's coat, whatever it is Write it down by squaring it, the formula is now ready Take the turn, the formula is ready, it's okay now roughing it and moving forward like if we talk about it mine a our If the noise is taken out of the equal if mode This will become positive mode is always positive value returns what mode always returns positive value then p is equal to what a What will you call this? Will you call this constant? What will Constant say? This is what he will say What do we need to tell about the distance constant It has been proved, now solve the next question Let us do question 10 Note down this much so that you can solve 10 questions yes, take a note quickly till then we will rough it out If yes, please note it down quickly and then like it If you haven't done it, please like the video You must give the video to all the students Liked it do questions 10 Question 10 is the turn and we will not do it We would have written any question 10 along with it okay question 10 said it has been said that we have to prove what we have to prove I write it and then explain it to you this time I gave you lips, what did you give me this time gaya lips given by ex squad's own A [ __ ] Pwa [ __ ] K Apne B [ __ ] Ew The length the length of normal the length of normal Varies this will tell the meaning of Varies Ivers it is written inversely here s The write down perpendicular Perpendicular from the Origin From The The Origin of the Tension on the Tenth It now let's explain it to him what to do now let me explain it to you brother if we talk about it do For question 10 it said proven what do you want to prove, these are these lips, What are lips and what will you call them You will say curve, it is the equation of the curve Because the highest power is two or greater than two then that equation should be We say equation, further it is written whose length Length Length of normal to length of normal you already know the formula look length of normal wa route in wa's upon mendi x's hole Square It in Basic You remembered the length of normal correctly If so, the same is said about the length of normal find If you do it, you will find the use of the formula and then further wrote varies inversely varies means different what does it mean if it is different then we write it here where But write it up, write it down, this arrow goes up Showing different okay barricade means different and inversely inversely means Inverse means one is above and the other is below Happen Needed Perpendicular Perpendicular means this Perpendicular distance to distance for this this word is used from the What to do with Origin Origin find the perpendicular distance Find the Perpendicular Distance from the Origin tange of tange means equation Off You have to find the tangent equation of tangent This formula follows from the formula The formula is tent. The meaning of this equation is Finding an equation using a formula when If the equation comes then it is perpendicular to the origin If you want to find the distance then use perpendicular The distance is this and the normal length is this Length if so then it is said that varies inversely Inversely means the betel leaves made one above the other If it remains then the normal length will remain above and its length will be below tenge okay so Here you have to write like Let's write Perpendicular in short Perpendicular Distance From Origin From Origin on the tange means to prove this what to do have to proofread it is proved, if you want to prove it then what else You people could not understand the issue of barricades I mean like the answer sheet that will come out as if a b c came out as if a b c came out You will know only after you shed a tear but here But for our explanation, here is the answer sheet Like A B C which came out of it hey and take the pakka pakka okay so reez this is what it means to be different from each other should mean in its answer sheet and its The answer sheet should contain some items like Here there is B and there is B and the rest are different hey look it said Different A and And I'll show you this fraction by doing it like this This means there is some change in the answer sheet you will get something you will get the same berry means this It happens, I understood, now there will be no problem Now let’s get this done Solve first of all you have to write the lips The Gavin Curve Write the Given curve curve means lips lips are y But lips are a curve, then X is a square a [ __ ] in the apon of the pwa [ __ ] in the apon of the be square ive a point what should i do point because when we get to know your ex will take out So we definitely need points if yes then tell me its parameters of these lips tell me the parametric you will remember a cos theta b If it was a sign then it would have been fine if I had written it here Are Parametric The equations are parametric equations e take a cos theta and b sine theta of wa value a cos theta b sine theta this Lips are parametric, these are Everyone has four, circles have four. also remember You should also remember about parabola You should also remember the lips of hyperbola You should also remember conic in class th If you have read the section then read it again. what's the problem okay so here's what we're gonna do we'll take out d one because d up d one If we talk about this formula then we have If you want to use it then it is differentiable Again it will happen and equal to zero constant Now here the service of UPD is zero Let's find out the value of yourselves square to its d equals minus 2 A [ __ ] in the ap of x cut it do tova upon mendi x ke equal hai minus of b square x in upon a squa ok so come on Gaya 2 to 2 got cancelled for B Squad crossed it into and below it okay now we have to find the length of normal length of Normal to equal wa and root na plus d wa k upon x equal whole square now Look at y, put the value of va from here b Write sine theta and not the plus root of put in the value so b square of minus is and put in the value of one this is the value of one put this in here so a cos theta a cos theta upon has a [ __ ] a [ __ ] and ba also there is ba's value put it from here b sine theta then v sine theta and whole power to Now do a lot of hard work, one from top to bottom went a b up and down now what I got If we solve that then what is the plus on top come v square cos square theta okay Because give me the power, this is two whole power right? If you give it on B, then give it on B square So curse square here so give me a square and Here we will give the sign square theta now LCM take what take LCM OK NOTE do it now let's rough it out, what should we do Let's do it rough So get it solved here But okay, after that I have to write from here so v sine theta we will write it from here because we need space should okay so v sine theta and lcm when will take a [ __ ] sine [ __ ] theta a [ __ ] if you sign in to this then a sqa sine square theta plus b Square and Kos Square theta so you know it's gonna come out sine sine theta by theta will cancel out so v sine theta upon a sine theta means a the [ __ ] is out If it comes out then it will become A and in the root it will be A square sine square theta plus b squa to squa theta okay this cancels So if you do that, you have a square root of v and a root of v. sine square theta plus v square cusp square theta it means to put this equation This is the length of the Normal Length of Normal is Equation First Now give us the tange perpendicular distance To find out the tensity, first find out the equation write its download sheet here because put it first in the equation Neither when we show the verries Use of first and second inverse equations If you want to show me how to do it, then let's write it here Length of normal length of normal v k up a and root of a square cy square theta ps v [ __ ] and we put this into the equation First, now we have to tell the equation Firstly, because we have distance from the origin have to find If we talk about perpendicular tent then the tent equation is as follows: so just take it out It will be fine, so find the slope first what take out the slope take out the slope of the tent so here we are will write slope off tent at point bolo parametric jo likhte write down the same a k theta ka v sa theta okay so tell me now brother slope m's in equal dy1 dx3 and where v is the theta okay so dydekop.org This one, you have to put the value of x in it this has to be placed in the place of y and this in the place of y I have to keep it, okay, we'll rough it out okay brother keep it so minus ka b square ex The value is a of theta and upon a the value of squa from here b sine theta do katta pitti from b b went from a A is gone so what will we get above minus b cos theta and below is the sine theta formula now put the equation off tent equation of tent at point take this b sine of a cos theta theta a cos theta b sine theta so formula hai wa minus ka vav e x minus xv okay put the value this this is xv this is wow note it down Now let's get this solved further let's get it solved further, okay Tova value of minus vav b sine theta equals a The value of is i cos theta upon a Sign The value of theta x minus x is a cos theta now turn the cross into what should I do cross into tax two so ava sine theta minus ae sine sum it into square theta equals b x cos theta minus minus of two plus a cos square theta ab of x and You have to write the term of wa near x and I want to write the term pass of wa ok will write We'll rough it out now look at the term x on this side then we will bring v x cos theta and add this to v sine theta and equals it will go to no so a Also take the common one as it also has this In this also cos square theta is found from here And what did you get from here minus minus is plus this is the formula sine square theta ok so how was x plus ava sine of theta equals a in a what is the sine square of the ps cos theta if there is a forest then write it here b x cos theta plus ava sine theta and we'll bring it to this side because if a matter of distance What should we talk about, perpendicular distance a matter of Do this thing only after making it equal to zero We have told you ok you need to remove it from at origin perpendicular The distance is here I will write it, write it perpendicular, you also write it perpendicular Distance Perpendicular Distance From Origin on the tent on the tent okay so best among equals What you need to do first is Origin Do you know the value of zero of zero then the value of x Put zero then the value will be zero in it Put it in and it will become zero minus a k upon I have to write a coffee what to write kont Do you remember the formula? 0 is xv vav if we calculate the distance So the square is written in quad root So what is its co-efficient square and write down one of v is theta so b sc cos sqa theta now the coefficient of y got the coefficient of va so okay now this take the mode because distance is never is not negative now let's rough it out now look here what to do like if we talk about mode If you open it then it will show plus only then v square cusp square theta plus a square and sine square theta it What equation do you put? Put two seconds. Now see. Here the barys is written inversely which The answer sheet has arrived and it has some common features you will find something different, you will find the meaning of barricades If you find something different then look at the root look at the root of b square cos square theta matched plus a sine theta matched Something different There will be something common, we will get berries, it means If he removes this barrier then the whole match will be over there should be the complete match there should be the top and below means perpendicular that is one above and one below means normal if We have to prove the tent is perpendicular So the normal eye shut will be on top and the tense will be equal to the value below if this barricade is not If it was written then it would have to be matched same to same what is its should come to it but If it is written barrij then it means something different will remain different then b has its a and here ay It is different, some beans will remain, so I got this bean So if you wanted to prove this, you had to write it down from equation first and second to from equation first and second So write the length on y off length off Normal Equals One Upon perpendicular Distance Perpendicular Distance from origin on the Tange on the tent it's cleared okay so in the box We take it because it is what we need If you wanted to prove it then note down the question Let’s get it solved Next quickly child take note next the question is No one will turn with him what is question 11 Is We will explain that to you a little bit It is a long question but it is simple and not tough if you have studied the basics it is not tough The question is very simple if you have studied the basics the question is Simple Lollipop is a lollipop brother, it's very simple The question is simple so if we talk about 11 If we do it then it is said here in the curve Write in the curve, all students write if do not book your Next to it is written Prove to prove it portion prove the portion of The tange of the Tange Intercepted Intercepted between the between the Coordinate Access Judge Access Judges Divided At it's point of contact into segment into Segment into is written here But it's okay, change the marker a little more. after the segments are written f are in A Constant Ratio brother tell me how will you solve it like here But I said in the curve, I have this curve have to prove it using this curve Now portion means that like x up a ps y up be ive this is the equation off line is equation off line in The Intercept Form The Intercept Form Is The diagram is this What does portion mean? This portion is said to be This portion gets intercepted this portion was said this one this These are the intercepts of the axis What are the meanings of axis people intercept x axis like ya axis it there are intercepts and this portion is said Went portion this one portion of the tenge Intersect So look at the intercept, what does it mean to intercept It means he told it was intercepted so whether it is intercepted or not this is said this is said this what is this They say they make you a little bigger to explain So this is what we call intercept this is what is called the x axis The intercept is of the y axis, it means Between these two there is coding access one here is the coordinate Access is further written is divided at its point like here take any point take points like x1 and wow took it here But I told you only this point Divided Meaning of Counted Into Segment Segment It is a part, meaning it is called a segment This means segmenting the portions segment means part so do one this one this is ok So here A and B mean P p ratio pabi it is said p ratio pa b It is said that the ratio should be constant Constant means there should be a constant Whatever comes out, this is the constant proof have to do something understand pareo If you want to do constant proof then you have to do this First, we have to find an equation by type because this is what happens from here to here then A gets zero and B is whatever happens is below the y axis so the y axis is the distance of what is written below y the distance of the axis is the distance below the x It is written that it is the distance of the x axis, so So from here, from the origin to A, then A is 0 From origin to B then GB then this will give you You have to find it here, we have it with us This is the equation of intercept but You have to make it, it is clearly stated You have to find out the tenge tenge in this way I want to find it, I will find the curve, I have it remember the formula too let's rough it out if we understand it Proofing the Perio Pvi Constant Hey brother, see how the constant will be proved Given Curve write down the given to solve this are the remove the given curve this is ok the given Write the curve to the power of x in wa Take this many points in the power of equals One has said that the point of contact point Off contact means one point contact Contact should be in contact the contact is written correctly there should be a point in contact then We took it as if no one told him keep in touch keep in touch Keep this point in case you need it We have taken it, if you need it then what will you do If you want to do equations then you have to use them This is okay so the points will be these ones But the slope has to be found at this point If you want to find the slope then for the slope you will need Differentiable There is power on both sides so log in take log x to the power of a and y to the power of a I have m and one has a so pay attention put in equals log a to the power of a p a then What do the formula log a of log a and log a to the power m p a log a in equal The power comes forward in me, if you move it forward then m log of x plus n log get n log of m ps A now Differentiable of a plus n lagwa equals in m plus of a first d od one keep it and put m plus a in a now see How will you make the difference, it will happen This much and this much will happen but wa what will happen again and make it equal to zero why is it constant what is it constant isn't it true that the constant has zero if we wa k talk about your dx in equal minus ka apn x tova k upd x If you take out the minus then this thing is in Ava's app send it then find the slope of n x xv Kama wow let's rough it out what do we do with it, let's rough it out now Deriving the Slope are slopes Off tent slope of tent we said like You have to find the equation whether it is for a tent Find the slope of the normal You have to find the slope of the tangent only You have to find out even if there is an equation in the question If you ask about normal or tent then that is why we Take out the slope of the tent here Slope Ava's Upon Mendy x x v kama wow ok keep that answer sheet in place of wa and in place of x use xv now Take the Equation of tent equation of tent at xv vav formula lagawa minus vav e in a into I'm getting this much wa minus wav now put the value of a do ae wow apna ae xov x minus k xv now cross into two cross into Creating an intercept form by This means finding the equation of tange If there is an equation of tangent then we have to find it but in which form do you tell which form I have to find it in intercept form means you have to bring it in this type because Do you know its diagram here a comma 0 and here 0 b means this type If you take it out from here then make this diagram Then you know we can divide this line in ratio If you want to prove it then look here, cross into if it will be Ava Ava xv and this is going to be minus n xv wav equal now its into this do it so minus m is one wave minus m x vav its into me plus m xv vav to x term and va to pass term If you want to keep it close then bring it to this side m ax Vav is the term of yeva then ava xv equal If I take it to that side then take the common take it like this xv in y1 in this x1 It is a new thing, if we take it to that side then it is common Take it and you get m p a now divide it because what is needed and wanted in equal m x wav ps ka ava xv ap m p n xv y1 ew now we need a plus in the middle so the lcm return it once, write to it I have to write this once upon this and There is a slight miss print here. Ava Xv will be lcm will return m x vav ap m plus ka a xv wav ps ava xv apn m plus ka a xv wav ive been so clear now look at y1 to y1 cancels xv to xv cancel now look here x and y here x and y are alone here x and y If you are alone then you have to be alone here too Because right now there are two bananas here This is a banana x and there are two bananas here too because n is going into and m is going into If it is left then there are two bananas, what do I need If you want to be alone then do this to make me alone for this a take it down like this a give it down okay Let's rough it out Let me tell you now how you can fill it in this form If you want to convert then m plus one upon one ka a eq is okay this will come down m a Gone is ok now see the plus there Take Wa's apon wa ke apon a plus ka a and bav ke Up I take this down so a equal in no ok this is how the diagram is formed now Make it a little from this side Let's make a little from this side these are the x axis I took it and I took this axis is okay and this is the intercept for mean This is the equation of the line, so I took it here on and here you know x's upon a So here I get the zero of A. Whatever you have, write that much, if there is any zero then write A plus ka a into me xv ap A okay here comes the b of zero zero Kama is under Ba, same comes under Ba what is there will come so a p a wow our a and here we take p xv wav this We had late the point so P and P B means a take it b to p re p b constant Distance formula is to tell the ratio It means whose formula will determine the distance Look, you will remember the formula of How do we explain the distance formula sesse xv and wav is okay and here x2 and two take this distance This is a formula brother, it is broken from here to here what is equal to xv minus ext Whole Square and Plus Vav Minus Vatu Ka Whole square this formula in two points It is used to mean this point and this point If you want to find the between then this is the formula If so, we will use this formula here Look at your P, B means we have ratio If you want to extract the constant then do it separately above put it up and down put it separately put it up separately put it down If you put it separately then minus the next one and see xv minus ext then this is from xv If you minus the x then what is the minus a plus a into xv my a and hole Square Hole Square Dekho Na Xv My ext's hole square then vav mine 0 Whole square of plus vaw minus 0 Distance formula has been used in PP if you use p b then remove the zero from the aqu If you minus it, then the square of x = minus 0 plus wav me this minus do it tov minus a plus of a into me wow upon me this a and its hole square okay now look we simplify let's do this then p's upon p's be equal I'll take out the xv from here so the xv [ __ ] Come Now we got here minus a plus a This is what I got in my apk, look at this xv If you take it out then it will bring this power here and so much of me is fine and this Keep the square like this in the root upon the Look at this here xv square here wow take it out wow take it out so What's left in the bracket, he will bring his power n minus a plus ka a k in its l square okay one line and write here If you go then your pub is equal to a little here Simplify it take the LCM so m then m the whole square of minus m and minus n ps y1 sqa now take the lcm down also So write x1 square like this, come here are y1 squa n turn this into this n minus m minus n whole square this cut minus n plus n and plus If the A of the minus is cut off, then the A square here Our A squad will come, okay let's rough it out yes take a note, now I will tell you a little from here we need to find the constant ratio What to find in Constant Ratio Finding so is p's own pb going on what is going on I am writing to your P B, okay now write on this in the name of P B so above xv square and what here The square of minus a will turn out to be n A square and a plus in the upon of the square Square Apk x1 here [ __ ] just like that write plus here wow [ __ ] write like this and what will come in into my a if its a m [ __ ] up n [ __ ] will come this is the minus this is the power to plus You will get the root, apply the root then p in the up of p what do you write in the name of p take the sacrifice and equal lcm if take m scale over what We'll get n s x1 s plus m s y1 s now. take the lcm below take both places above down Here you get the n below, put it into this so a squa xv squa plus its a squa wow square okay now this is You took the LCM, this one will go up, this it will go to the top it will come down so up of p p b and you have to remove the root also, did you remove it If you want to give route then this will go up your route will delete okay so write this down a [ __ ] xv [ __ ] plus a [ __ ] in a sentence it will come down a now look here a squa xv squa plus a [ __ ] baw [ __ ] now these same two It is the same bracket, look at the first term first term second term second term mass ho Now whatever has come is upon me B has come upon A so if we talk about what did the p re p b ki come out aye reyo ae to This is a constant, there is no variable in it It seems this is what was to be proved had to prove that P re P B is equal to A Re A if you wanted to prove this then you should have done it in this class Let's keep the questions till question 10 here You should have checked whether question 10 was asked or 11 was asked How many questions are there till question 11 It's over in the next class beyond this will get the question solved You guys complete this much by taking the next class If you come and get the question solved then you will guys please complete this if this is my class If you like it then please like the video and share it Share the video as much as possible See you next in my friend circle That's enough for today in class Thank you [music]