Geometry

Question Analysis

The main focus is to convert the given circle equation from general form  to the standard form  by completing the square for both  and  terms, and then determine the radius .

 

Key Concept Explanation

For a circle in general form , we complete the square for  and  terms. For , we add , and for , we add . In the standard form ,  is the radius of the circle, which is the positive square root of the constant on the right - hand side of the equation.

 

Step-by-Step Solution

1. Rearrange the given equation to get all terms on one side: .

2. Complete the square for the  terms:

The coefficient of  is . Half of  is , and . Add  to both sides of the equation.

3. Complete the square for the

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