What is the center or a circle represented by the equation (x+9) 2 + (y-6) 2 = 10 to the power of 2

(-9,6)

Step-by-step 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)