Question

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

Answer 1

Answer:

(-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)