Geometry

Question Analysis

The main focus is to find the center and radius of the circle using the endpoints of the diameter and then write the equation of the circle 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 the circle is the midpoint of the diameter, and the radius is half the length of the diameter. The midpoint formula for two points  and  is , and the distance formula between two points  and  is .

 

Step - by - Step Solution

1. Find the center of the circle:

For the endpoints of the diameter  and , using the midpoint formula , we have  and . So the center of the circle is .

2. Find the radius of the circle:

Using the distance formula to find the length of the diameter between  and , . The radius