[Music] hello makawamat in this video lesson we will discuss the continuation about circles but this time we focus on the general form of the equation of a circle write the equations in standard form and find the center and ranges of the circle but before we proceed to our discussion don't forget to like our videos and subscribe nerinkaya the general form of the equation of a circle is x squared plus y squared plus dx plus ey plus f is equal to zero so pan banana so from standard form of the equation of a circle indeed derived not in your general form of the equation of a circle so babali cannot end so from the standard form of the equation of a circle to general form of the equation of a circle so given the equation of a circle so under nothing i go and expand not a new square of binomial so pano battalion expand and square a binomial so first we need to multiply nothing in first term so x times x that is x squared and then multiply them first and last term not and multiply it by two notepad so x times negative h that is negative x h times two so that is negative two h x and glass so multiply the last term twice so negative h times negative h that is positive h squared so same process of y minus k squared so x plus y squared minus two k y plus k squared is equal to r squared so after nito after nito we are going to combine and then simplify all the terms but this time so let so on in munich combine money in new mega terms and then arrange not n so after that in my arrange so that is x squared plus y squared minus two h x minus two k y plus h squared plus k squared is equal to r squared and then leap but not and say r squared d to the left side okay so omega squared plus y squared minus two h x minus two k y plus h squared plus k squared minus r squared is equal to zero so if d is equal to negative two h and e is equal to negative 2k so let d is equal to negative 2h and e is equal to negative 2k and f is equal to h squared plus k squared minus r squared so papadi so x squared plus y squared and then your negative two h x naught and magnitude plus the x naught because nothing negative two h sub d so that is plus dx and then same with negative two k plus e y so it up in eternity negative two k now e so that is plus e y plus you know h squared plus squares k squared naught and minus r squared pinellita not in an f so from the standard form of the equation of the circle to general form of the equation of a circle so write the general equation of a circle with center of four and negative one and a ranges of seven units so much star ties uh standard form and circle so h naught in d is positive four and your k nathan is negative one and the radius seven units or r is equal to seven so from the standard form of the equation of the circle is a substitute nothing in value than h nathan and k at the same time young radius net n since young h net is positive so mug again x minus four squared plus young k nathan is negative one so negative times negative one that is positive one so y plus one squared is equal to young radius not in a seven so that is seven squared so seven squared that is 49 y so 7 times 7 is 49. so after nito expand nothing in square of binomials it's expanding nothing you square a binomial not n so x minus 4 squared that is x times x that is x squared x times negative 4 negative 4 x times 2 that is negative 8 x plus negative 4 times negative 4 that is positive 16. so same sub uh young gaga means a y plus 1 squared so y times y that is y squared y times 1 that is 1 y or y n times 2 that is 2y plus 1 times 1 that is 1 copy 49. and then after that uh ngagoen arranged not in terms so we arranged nothing in terms to general form so i'm again x squared plus y squared minus eight x plus two y plus so simplifying antenatal so lipanity and forty nine dita lepside nathan so 17 y so 16 plus 1 that is 17 minus 49 so problem here so nili but not in skynet bug inside it equals to zero so simplify 17 minus 49 that is negative 32 so the general equation of a circle is x squared plus y squared minus 8x plus 2y minus 32 equals to zero so i'm going along sundan yulang in general form arrangement on general formula equation and circle so molasses standard form square language binomial and then arrange nathaniel terms paramagne general equation or in general form the equation of the circle next is right x squared plus y squared plus six x minus seven equals to zero standard form so caballita from general form to standard form so pano natin gagawan so this time class during grade nine how to solve quadratic equation by completing the square so nothing again how to solve a quadratic equation by completing the square from the given we have x squared plus y squared plus six x minus seven so on gaga in munich x terms nothing at once y term since x terms not and so nothing so x squared plus six x plus y squared is equal to seven so muladito young x squared plus six x and gaga in your class because if you perform that and you're completing the square so pandubagi nagaway i'm completing the square it don't need the term not n okay in middle term that and indeed divide nothing by two if you divide by two tapusions i got it squared not n so six divided by two the answer is three that was squared nothing you said nothing at three so three times three that is nine so nothing squared quadratic equation and so in quadratic nothing so x squared plus six x plus nine so plus nine so i'm getting class six x pinner formulating and completing the square parameters a perfect square trinomial now so but perfect square trinomial pretty nothing going square or binomial though uh that is three since positive being signed so pagina one nothing square or binomial to magicking x plus three squared plus capital and nothing and y squared then seven plus nine is equal to sixteen so it only only standard form non equation atom so again uh paramagnet square binomial and individual at n squared union again at ten so since three on so making x plus three squared plus capping along and then you somnito that will be our standard form another example right x squared plus y squared minus 4x plus 18y plus 35 is equal to zero is in standard form again so muladito paksasa mahinate so mugging negative 35 again x terms y terms and then after nito after your middle term that ends at 2 so that is negative 4 divide 2 the answer is negative 2 tables squared not a negative 2 times negative 2 that is positive 4. so a b sub n positive 4 right side not n next the tournaments are y terms so 18 divide two that is nine so nine squared nine times nine eighty one so a big sub and a degree indeed is eighty one at mcdonald's eighty one so parang anytime you are a class so the negative nothing in four right side it did nothing in four seconds 81 then after that since perfect square trinomial neto gaga we nothing square of binomial so nothing can enable negative two on so i'm again x minus two squared plus so nine so y plus nine squared is equal to negative 35 plus 4 that is negative 31 plus 81 that is 50. so itunes standard form now equation of circle net n the quantity of x minus 2 squared plus the quantity of y plus 9 squared is equal to 50. another example what is the center and the ranges of the circle so this time an inner hand of the man given in general form the equation and circle net n and hinahana pissing center and ranges of the circle so x squared plus y squared minus six x minus ten y plus eighteen y eighteen is equal to zero so on uh nothing on completing the square so panel divide nothing in middle term nut and satu negative 6 divide 2 the answer is negative 3 squared not n negative 3 times negative 3 that is positive 9 and then d twos are y terms now then so negative ten divide two the answer is negative five negative five times negative five the answer is positive twenty-five so in nine zero twenty-five right side not n right sideline equation so i'm getting x squared minus 6 x plus 9 plus y squared minus 10 y plus 25 is equal to negative 18. so ityon plus nine san galingo nine young mandito opposition twenty five eight dagdagnath so problem square oh a perfect square trinomial giving nothing square of binomial so i'm again quantity of x minus 3 squared plus the quantity of y minus 5 squared is equal to 16. so and after that since hindi paito young regis nathan so on gagoinaten is square root panation c16 so on a square root of 16 not then so that is four so eb sub n x minus three uh the quantity of x minus six three squared plus y minus five squared is equal to four so you center nothing since that indication center at your not in a4 so given general form circle center and regis so another example finding the center and ranges of the circle given the general form of the equation of the circle so measured uh another major challenging and nothing given time y squared so 4x squared plus 4y squared plus 12x minus 4y minus 90 is equal to zero since so 4x squared divide 4 that is x squared delang so ma concilium 4. 4y squared divide 4 so y squared then on my e1 12x divide 4 that is 12 divide 4 that is 3x negative 4y divide 4 so negative y is equal to 90 divide first so that is 90 over 4. so it only in a meaty nothing equation x terms not n so that is x squared plus three x plus blank and then y squared minus y plus blank is equal to 90 over four so we not going to get nothing completing the square so three divide two so that is three over two no and then squared not n three three times three that is nine two times two that is four so in three over two squared is equal to nine over four and this habit negative one over two that is negative one half negative one half squared so that is positive one-fourth so is nine over four detent amount one fourth so same didn't do right side not n so that nothing nine over four and then one fourth so mug again x squared plus three x plus nine over four plus y squared minus y plus one fourth is equal to ninety over four plus nine over four plus one over four so negative fraction with the same denominator so madali add nothing like the numerator not then divide it by four so 90 plus nine that is 99 plus 1 100 100 divided four the answer is 25 so going at the square by dom although so x plus three over two squared y minus one half squared is equal to twenty-five since independent radius is cooling for nothing square root of twenty-five so square root 25 is five so e-big sub-n the quantity of x plus three over two squared plus the quantity of y minus one half squared is equal to five so your center nut and a negative three over two okay take uh take notes assigned classes is negative so negative three over two and then your y naught is positive one half so your radius net n is five so the yangnyeom company given the general form of the equation of a circle thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button but updated ko for more video 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