Question

The equation for the circle is:

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.