Question

what is the center of the circle described by the equation $(x - 2)^2+(y + 7)^2=169?
a (2, 7)
b (-2, -7)
c (2, -7)
d (-2, 7)

Explanation:

Step1: Recall circle - equation form

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

Step2: Identify h and k values

For the equation $(x - 2)^2+(y+7)^2 = 169$, we have $h = 2$ and $k=-7$ since $(y + 7)^2=(y-(-7))^2$. So the center of the circle is $(2,-7)$.

Answer:

C. (2, -7)