Question

find the center(h,k) and the radius of the circle with the given equation: x^2+y^2-4x+18y+85=36

Answer 1

do you know how to complete the square? you have to do it twice, once for \(x^2-4x\) and again for \(y^2+18y\)

Answer 2

(x-2)(x+2),(y+9)(y+2)

Answer 3

no that is not quite right
\[x^2-4x+y^2+18y=-49\]
\[(x-2)^2+y^2+9)^2=-49+4+36=-9\]hmm we have a problem, because the left hand side is negative are you sure this is correct?

Answer 4

no im not sure than

Answer 5

oh wait i made a mistake sorry

Answer 6

\[(x-2)^2+(y+9)^2=-49+4+81=36\]

Answer 7

where did the numbers come from? \(-2\) is half of(-4\) and \(9\) is half of \(18\)
that is how you complete the square. on the right \(4\) is \((-2)^2\) and \(81\) is \(9^2\)

Answer 8

got that part

Answer 9

now we can read off the answer
\[(x-2)^2+(y+8)^2=36\] compare with \((x-h)^2+(y-k)^2=r^2\)

Answer 10

got it so it wold be (h,k)=(2,-9) radius is 6

Answer 11

yes you got it