Geometry

Question Analysis

The main focus is to transform the standard form of the circle equation, given its center and radius, into the general form and identify the correct option among the choices.

 

Key Concept Explanation

The standard form of a circle's equation is , with  as the center and  as the radius. The general form is . To obtain the general form, expand the standard - form equation and simplify.

 

Step - by - Step Solution

1. Write the standard form:

Given the center  and radius , the standard form is .

2. Expand the equation:

Expand  and .

Then .

3. Rearrange to general form:

Combine like terms: .

Calculate

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