Question

what is the center of the circle with the equation (x + 8)^2+(y - 6)^2 = 36?
a. (8, -6)
b. (8, 6)
c. (-8, 6)
d. (-8, -6)

Explanation:

Step1: Recall circle - equation formula

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Rewrite the given equation

The given equation is $(x + 8)^2+(y - 6)^2=36$, which can be rewritten as $(x-(-8))^2+(y - 6)^2=6^2$.

Step3: Identify the center

Comparing with the standard form, we have $h=-8$ and $k = 6$. So the center of the circle is $(-8,6)$.

Answer:

C. $(-8,6)$