Geometry

Question Analysis

The main focus is to determine the center and radius of the circle from the graph and then convert the standard form of the circle's equation to the general form.

 

Key Concept Explanation

The standard form of a circle's equation is , where  is the center of the circle and  is the radius. The general form is . We expand the standard form to obtain the general form.

 

Step - by - Step Solution

1. Identify the center and radius:

By observing the graph, the center of the circle  and the radius .

2. Write the standard form:

Substitute into the standard - form equation: , which simplifies to .

3. Expand to the general form:

Expand  using