Geometry

Question Analysis

The main focus is to determine the center and radius of the circle from the graph, then write its standard - form equation and convert it to the general form to match with the given options.

 

Key Concept Explanation

The standard form of a circle's equation is , where  is the center and  is the radius. The general form is . We expand the standard - form equation to get the general form.

 

Step - by - Step Solution

1. Determine the center and radius:

By observing the graph, the center of the circle . The radius  (estimated from the grid).

2. Write the standard form:

Substitute , , and  into the standard - form equation . We get .

3. Expand to the general form:

Expand  and .

Then .

Rearrange terms: