Question

The equation for the circle is:

x² + y² + 16x − 24y + 159 = 0 .


What is the center of the circle?

Explain Your Answer. Thank You ^-^.

Answer 1

(-8,12)

the equation for a circle, centered at (h,k) with radius r is

`(x-h)^2+(y-k)^2=r^2`

so you need to get your equation in this form. completing the square is one way to do this. separating x and y terms you get

`x^2+16x+y^2-24y+159=0`
which can then be rewritten using complete the square

`x^2+16x+64+y^2-24y+144+159=0+64+144`
which is equivalent to

`(x+8)^2+(y-12)^2+159=208 \\ (x+8)^2+(y-12)^2=49`

so your center is the point (-8,12) and the radius would be 7.