Geometry

Question Analysis

The main focus is to convert the standard - form equation of a circle, based on the given center and radius, into the general form . This requires expanding the standard - form equation and simplifying the terms.

 

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 is . To get from standard to general form, we expand the squared binomials in the standard - form equation and combine like terms.

 

Step-by-Step Solution

1. Given the center  and radius , the standard - form equation of the circle is .

2. Expand  and  using the formula :

 and .

So the equation becomes .

3. Rearrange the terms to get the general form:

Combine the constant terms on the left - hand side: .

Calculate , resulting in the equation .

 

Option Analysis

A.

Click "Show Answer" to reveal the answer and analysis