Geometry

Question Analysis

The main focus is to convert the given circle equation from general form to standard form. We need to complete the square for the - terms in the equation to match the standard - form .

 

Key Concept Explanation

The general form of a circle's equation is . The standard form is , where is the center and is the radius.

 

Step - by - Step Solution

1. Given the equation .

2. Focus on the - terms .

To complete the square for , we take half of the coefficient of , which is , and then square it: .

Add 36 to both sides of the equation: .

3. Rewrite the equation:

The left - hand side can be factored as .

The right - hand side is .

So the standard form of the equation is

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