Geometry

Question Analysis

The main focus is to find the general form of the equation of a circle given its center  and radius . We need to first write the standard form of the circle and then convert it 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 of a circle's equation is . To get the general form from the standard form, we expand the squared terms and simplify.

 

Step - by - Step Solution

1. Write the standard form:

Given the center  and radius , the standard form of the circle is , which is .

2. Expand the standard form to get the general form:

Expand .

 and .

So .

Rearrange the terms:

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