The problem asks for the equation of the circle shown in the graph.

1. Problem Description

The problem asks for the equation of the circle shown in the graph.

2. Solution Steps

First, identify the center of the circle. From the graph, the center appears to be at the point $(1, 2)$.

Next, determine the radius of the circle. The radius is the distance from the center to any point on the circle. The circle appears to pass through the point $(3,2)$. The distance from $(1, 2)$ to $(3, 2)$ is 2, so the radius is

2.

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

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

In this case, $h = 1$, $k = 2$, and $r = 2$. Substituting these values into the equation of a circle, we get:

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

$(x - 1)^2 + (y - 2)^2 = 4$

3. Final Answer

$(x - 1)^2 + (y - 2)^2 = 4$