The general equation of a circle is: where is the center and is the radius. The center of the circle is the midpoint of the diameter. The extremities of the diameter are given as and . Step 1: Find the center of the circle.
The center is the midpoint of the diameter, so we calculate the midpoint of and using the formula for the midpoint: Substituting the values: So, the center of the circle is . Step 2: Find the radius of the circle.
The radius is the distance from the center to either endpoint of the diameter. Using the distance formula, we calculate the distance between and : Thus, the radius is . Step 3: Write the equation of the circle.
The general equation of the circle is: Simplifying: Expanding the equation: Thus, the equation of the circle is .