Geometry

Question Analysis

The key is to identify the center and radius of the circle from the graph and then transform the standard - form equation of the circle  (with  as the center and  as the radius) into the general form .

 

Key Concept Explanation

The standard form  describes a circle centered at  with radius . Expanding  and , and then rearranging gives the general form. This process involves basic algebraic expansion and simplification.

 

Step - by - Step Solution

1. Determine the center and radius:

From the graph, the center of the circle .

Counting the grid units, the radius r = 5.

2. Write the standard - form equation:

Substitute , , and  into , getting

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