Geometry

Question Analysis

The main focus is to convert the given equation of the circle from general form to the standard form .

 

Key Concept Explanation

The general form of a circle is . To get the standard form, we use the method of completing the square. For a quadratic expression like , we take half of the coefficient , square it and add it to both sides of the equation. Similarly, for , we take half of , square it and add it to both sides. The standard form represents a circle with center and radius .

 

Step-by-Step Solution

1. Given the equation .

2. Complete the square for the terms:

The coefficient of is . Half of is , and . Add 25 to both sides of the equation.

Complete the square for the terms: The coefficient of is . Half of is , and . Add 9 to both sides of the equation.

The equation becomes .

3. Rewrite the equation:

Factor the and terms. We have .

Then