The problem asks us to write the equation of a circle with center $(-4, -6)$ and diameter 8. The given answer is incorrect.

1. Problem Description

The problem asks us to write the equation of a circle with center $(-4, -6)$ and diameter

8. The given answer is incorrect.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is:

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

Given the center $(-4, -6)$, we have $h = -4$ and $k = -6$. The diameter is 8, so the radius is $r = \frac{8}{2} = 4$.

Plugging the values into the general equation, we have:

$(x - (-4))^2 + (y - (-6))^2 = 4^2$

$(x + 4)^2 + (y + 6)^2 = 16$

3. Final Answer

$(x + 4)^2 + (y + 6)^2 = 16$