Answer:
(16, 30)
Step-by-step explanation:
First the equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2, where (h,k) - the center.
We rewrite the equation and set them equal :
(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2− 32x − 60y +1122=0
x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0
We solve for each coeffiecient meaning if the term on the LHS contains an x then its coefficient is the same as the one on the RHS containing the x or y.
-2hx = -32x => h = 16.
-2ky = -60y => k = 30. => the center is at (16, 30)