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The distance formula, midpoint formula, and center radius form of the equation of a circle are closely

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The distance formula, midpoint formula, and center radius form of the equation of a circle are closely related in the following problem.

A circle has a diameter with endpoints (-1, 3) and (5, -9). Find the center-radius form of the equation of this circle.

There are several ways to find the radius of the circle. One way is to find the distance between the center and the point (-1, 3). Use the result from Exercise 53 and the distance formula to find the radius.


Exercise 53

To find the center-radius form, we must find both the radius and the coordinates of the center. Find the coordinates of the center using the midpoint formula. (The center of the circle must be the midpoint of the diameter.)

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