The problem asks us to find the equation of the circle shown in the graph.

1. Problem Description

The problem asks us to find the equation of the circle shown in the graph.

2. Solution Steps

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

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

From the graph, we can identify the center of the circle as $(-1, 3)$. Thus, $h = -1$ and $k = 3$.

The radius of the circle is the distance from the center to any point on the circle. We can see from the graph that the point $(-1, 7)$ is on the circle. We can find the radius by counting the number of units from the center $(-1, 3)$ to the point $(-1, 7)$. The radius is $7 - 3 = 4$. Alternatively, the point $(-5, 3)$ is also on the circle, and we can count the number of units from the center $(-1, 3)$ to the point $(-5, 3)$. The radius is $|-5 - (-1)| = |-5 + 1| = |-4| = 4$.

Thus, $r = 4$, so $r^2 = 4^2 = 16$.

Plugging $h = -1$, $k = 3$, and $r^2 = 16$ into the general equation of a circle, we get:

$(x - (-1))^2 + (y - 3)^2 = 16$

$(x + 1)^2 + (y - 3)^2 = 16$

3. Final Answer

$(x + 1)^2 + (y - 3)^2 = 16$