The problem asks for the center of a circle with the given equation $(x - 5)^2 + (y + 8)^2 = 36$.

1. Problem Description

The problem asks for the center of a circle with the given equation $(x - 5)^2 + (y + 8)^2 = 36$.

2. Solution Steps

The standard form of the equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$.

Comparing this with the given equation $(x - 5)^2 + (y + 8)^2 = 36$, we can identify the center and the radius.

We have $(x - h)^2 = (x - 5)^2$, so $h = 5$.

We also have $(y - k)^2 = (y + 8)^2$. Since $y + 8 = y - k$, we have $k = -8$.

Therefore, the center of the circle is $(5, -8)$.

3. Final Answer

The center of the circle is $(5, -8)$.