Question

A circle has (-1, 1) and (5, -7) as endpoints of a diameter.

Find the center and radius of the circle.
Graph the circle.
Write the standard equation of the circle.

Answer 1

Explanation:

The center is the midpoint of the diameter, meaning that the center is (2, -3).

Using the distance formula, we get that the length of the diameter is 10, meaning that since the length of the radius is half that of the diameter, the radius is 5.

Using the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2, we get the equation of the circle is:

(x-2)^2 + (y+3)^2 = 25