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. This assesses the understanding of circle geometry and algebraic manipulation skills.

 

Key Concept Explanation

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

 

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 , which simplifies to .

3. Expand to the general form:

Expand  using the formula

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