Help find the equation of the circle that has a diameter with endpoints

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Step-by-step explanation:

The formula for the equation of a circle is:

where (h,k) is the center, and r is the radius of the circle.

To first solve this, we must use the endpoints of the diameter to solve the center of the circle using the midpoint formula, which is known as:

The points given to us are (12,8) and (4,6) so plug in the coordinates into the formula.

Center of the Circle = (1/2) * (-5 + -11) , 1/2 * (-3 + -3)

                                  = (-8,-3)

Now, to find the radius, we can use the distance formula, then use the center point of the circle (-8,-3) and one of the endpoints, (-11,-3). The distance formula is known as:

Radius of the Circle = √(x₂- x₁)² + (y₂-y₁)²

                                  = √(-11 - -8)² + (-3 - -3)²

                                  = √9 or 3

                                  =  r² = 9

Now that the radius and center are now known, the equation of the circle can be written as:

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step-by-step explanation:

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step-by-step explanation: