Question

1. what is the center of the circle with the equation ((x - 7)^2 + (y + 8)^2 = 49)?

a. ((7, -8))
b. ((-7, 8))
c. ((7, 8))
d. ((-7, -8))

Explanation:

Step1: Recall circle standard form

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

Step2: Identify h and k

Given equation: $(x-7)^2 + (y+8)^2 = 49$. Rewrite $y+8$ as $y - (-8)$, so $h=7$, $k=-8$.

Answer:

a. (7, -8)