Geometry

Question Analysis

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

 

Key Concept Explanation

The general form of a circle's equation is . To find the radius, we complete the square for  and  terms. For , we add , and for , we add . In the standard form ,  is the radius of the circle.

 

Step-by-Step Solution

1. Given the equation .

2. Complete the square for the  terms:

The coefficient of  is . Half of  is , and . Add 36 to both sides of the equation.

3. Complete the square for the  terms: