Geometry

Question Analysis

The main focus is to determine the equation of the circle in general form. We need to find the center and radius from the graph and then convert the standard form of the circle 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 of the circle and  is the radius. The general form is . To get the general form, we expand the standard - form equation.

 

Step - by - Step Solution

1. Determine the center and radius:

By observing the graph, the center of the circle is at the origin . The radius  can be found by looking at the distance from the center to a point on the circle. For example, the circle intersects the  - axis at  and  and the  - axis at  and , so .

2. Write the standard form:

Since the center is , the standard form of the circle equation is , which is .

3. Convert to the general form:

Rearrange the equation  to