Circle: Points on ends of diameter: Find the equation of the circle for which
the points (-6, 5) and (2, -1) are ends of a diameter.

The distance between these points must be the length of the diameter, or twice the radius.

From the definition of distance, we get

Hence the radius is 5. Next we need to locate the center of the circle, which is at the midpoint of this diameter. Using the definition of the midpoint of the line joining two points, we get for the coordinates:

, or .

Hence h = -2, k = 2, and the equation of the circle with the coordinates of the center as h and k: h = -2, k = 2: