Geometry

Question Analysis

The main focus of this question is to find the general form of the equation of a circle. Given the center  and radius , we need to first write the standard form of the circle equation and then convert it to the general form. 

 

Key Concept Explanation

The standard form of a circle's equation is , where  represents the center of the circle and  is the radius. The general form of a circle's equation is . To obtain the general form from the standard form, we expand the squared terms in the standard form and simplify.

 

Step-by-Step Solution

1. Write the standard form:

With the center  and radius , the standard form of the circle equation is , which simplifies to .

2. Expand the standard form:

Expand  using the formula , so .

Expand  using the formula , so .

The equation becomes .

3. Convert to the general form:

Combine like terms:

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