Geometry

Question Analysis

The main focus is to determine the equation of a circle in standard form by identifying the center and radius of the circle from its graph.

 

Key Concept Explanation

The standard form of a circle's equation is , where  is the center of the circle and  is the radius. The equation represents all the points  that are at a distance  from the center .

 

Step - by - Step Solution

1. Find the center of the circle:

By observing the graph, the center of the circle is at the point . So in the standard form ,  and .

2. Determine the radius of the circle:

By observing the grid, the radius  (since the distance from the center  to a point on the circle is 8 units).

3. Write the equation of the circle:

Substitute , , and  into the standard form. We get , which simplifies to .

 

Option Analysis

A.

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