For individual or collaborative investigation.ExerciseThe distance formula, the midpoint f...

For individual or collaborative investigation.

Exercise

The distance formula, the midpoint formula, and the 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.

Work Exercise in order to see the relationships among these concepts.

Exercise

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 your result from Exercise 1 and the distance formula to find the radius.

Exercise 1

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.)