[Music] hello makawamat in this video lesson we will discuss all about circles first let us discuss the overview of conic section and the definition and equation of a circle how to find the equation of a circle given this using the standard form given the point of a center and the reduce so but before we proceed to our discussion don't forget to like our videos and subscribe the ringtail so a conic section is the intersection of a plane and a cone observe the shape of the slice that results the angle at which the cone slice produces four different types of conic sections so young conic sections class this is the first topic nadi discussed a pre-calculus but uh focus circles so pakis so from the word kon so is [Music] circle so all about circle so a circle is consists of all points on the plane equidistance from a fixed point called the center so antagonitis is the center of the circle so the distance young distance from the center okay the distance from the center to any point of the circle is constant and is called the radius of the circle so on top of that it's a distance muladitos a center in a circle from any points of adding forms itoin postnatanza lesonatoriums equation a gamete in standard form no circle so the standard form of the equation of a circle is x minus h squared so you h is the value of x no center nothing plus y minus k squared so you can attend value x squared plus y squared is equal to r squared so tata and then net and a b seven zero zero center nathan find the equation of a circle with center at the origin and a ranges of five units so ibiza b and you [Music] origin which is zero zero and the radius is five so caps x squared plus y squared is equal to r squared so i'm twice uh linear five times five so that is twenty-five so equation that then the equation is circle and as a center you know you know center not an initial origin with radius of 5 units is x squared plus y squared is equal to 25 another example write the equation of a circle centered at 0 three and with rages six so hindi nasa center original center nothing so zero green up nothing yet any radius not in this time is six so applying the net in standard form of the equation of the circle so each net indeed is zero young k nathan is three applying the standard form the equation of the circle so x minus h squared plus y minus k squared is equal to r squared so hapaganito class capacitor in volume and h naught and automatic x squared delay n so r so that will become x squared plus y minus so papadi tanglang k so okay nothing is 3 positive 3 so y minus 3 squared is equal to so you are not in a 6. so 6 squared so 6 times 6 that is 36. so each equation of circle atom x squared plus y minus 3 squared is equal to 36. another example uh your center is at the two uh so it's a point two and negative five and with ranges of ten so your h naught n is 2 and you know a negative 5 so in your ages latin is 10 so apply the standard form of the equation of the circle so papalitan langnaten is a substitute netanyahu valued on h and k so since you h nathan is positive so x minus x minus parent minus perineum psi naught and nito so okay saying h nothing is positive so x minus two squared and uk nothing is negative since you know a negative so omega origin class negative net also negative times negative five because they compatible k so negative times negative five question again positive okay some other sub class a positive [Music] is 10 so 10 times 10 that is 100 so the equation is the quantity of x minus 2 squared plus the quantity of y plus y squared is equal to 100 another example so the center is at 1 5 and the given ranges is square root of 17 sopanito in this uh uh exact number or whole number no so marine time square root of 17 so pano gagawin so identify first the volume h that is one and the value of k that is five so substitute since young h9 is positive so that is x minus one squared and the nuclei nothing is positive also that is y minus five squared so papaya tendon is equal to so you are not in the square root of seventeen so capacitances uh no and then ma cancel nothing in two so mayweather seventeen raised to one so 17 raised to one seventeen or mas madingtan um and then in the squared miyan matatangalto so my e1 unisa so the answer will be the quantity of x minus 1 squared plus y minus 5 squared is equal to 17. so another example uh this time concavina uh given you center and radius nathan given in center in the circle radius x squared plus y squared automatic closing centroid nothing and zero zero okay so origin so x squared plus y squared is equal to r squared so your r squared not n here is 64. so panoramic 64. that is eight so a big subject equation not then is x squared plus so a mugging range is not in detail is eight okay so if it's a being in center net then okay and center and not then is zero zero and your radius snatting is eight units another example so the equation is x squared plus y squared is equal to 19. so same process since you center nothing in this origin so you point nothing on a zero zero so x squared plus y squared is equal to r squared so r squared nothing is nineteen so pan on it is square root log nathan young 19 so square root of 19 so what an exact number no square square root of 19 because it is a perfect square a per perfect number so as instantly in second not in the square root of 19. so in center nothing i zero zero so at numerators not n is square root of nineteen another we have x squared plus w the quantity of y minus two squared is equal to forty nine so x squared so x squared automatic zero yeah no so again nothing given that then so upon x squared you're given a b sub n and i zero so you h naught and a zero theta and then 49 i7 so in center net n i zero two also says zero two and then your radius naught and a seven next we have x or the quantity of x plus seven squared plus the quantity of y minus five squared is equal to fifty six since positive you say nothing back okay so negative seven and here since negative parenthood you can attend still positive so five parent and then kuninati in square root in 56 since the square root of the 56 freddy panetta may simply form battle so on gaga in lagnathan think of a number now perfect number sha now pagmi notifies a song number also got a 56. so anion 4 and 14 so 4 times 14 cassion4 perfect number yeah so ebik subbie and magua nothing square root 4. so in square root 24 is 2 square root of 14. so it didn't simply form me uh square root of 56 that is 2 square root of 14. so the center is negative seven and five and the radius is two square root of fourteen thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel