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 to match with the given options.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Determine the center and radius:

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

2. Write the standard form:

Substitute , , and  into the standard - form equation . We get .

3. Expand to the general form:

Expand  using , so .

Expand  in the same way, so .

The equation becomes

Click "Show Answer" to reveal the answer and analysis