Question

1. what is the center of the circle with the equation ((x - 4)^2 + (y + 5)^2 = 169)?

a. ((-4, 5))
b. ((-4, -5))
c. ((4, -5))
d. ((4, 5))

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 center from given equation

The given equation is $(x - 4)^2 + (y + 5)^2 = 169$, which can be rewritten as $(x - 4)^2 + (y - (-5))^2 = 13^2$. So $h = 4$ and $k = -5$.

Answer:

a. (4, 5)