Answer:
(-9,6)
Explanation:
The general equation of a circle is given as:
x²+y²+2gx+2fy+c = 0
The centre of the circle is (-g,-f)
Given the equation of the circle
(x+9)² + (y-6)² = 10²
First we need to expand and write it in the general form. On expansion:
x²+18x+81+y²-12y+36 = 100
Collecting like terms
x²+y²+18x-12y+81+36-100 = 0
x²+y²+18x-12y+17 = 0
Comparing to the general equation
2gx = 18x
g = 9
2fy = -12
f = -6
The center of the circle = (-g, -f)
= (-9,-(-6))
= (-9, 6)