Geometry

Question Analysis

The main focus is to use the endpoints of the diameter of a circle to find its center and radius, and then write the circle's equation in standard form.

 

Key Concept Explanation

The standard form of a circle's equation is , where  is the center of the circle and  is the radius. The center of a circle is the mid - point of its diameter. The mid - point formula for two points  and  is , and the radius is half the length of the diameter. The distance formula between two points  and  is .

 

Step - by - Step Solution

1. Find the center of the circle:

Given the endpoints of the diameter  and , use the mid - point formula.

 and . So, the center of the circle is .

2. Find the radius of the circle:

Use the distance formula to find the length of the diameter. .

The radius .

3. Write the equation of the circle:

Substitute , , and  into the standard form

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