The diameter of a circle has endpoints whose coordinates are r(-2, 2) and s(4, 2). find the equation of the circle.

Before determining the equation of the circle, we must determine first the radius of the circle and its center point.

Radius of the circle:
We find the distance between points R and S and divide it to 2. To find the distance between two points, the equation is

d = √[(x2 - x1)²+(y2 - y1)²]
d = √[(4 - -2)²+(2 - 2)²]
d = 6
r = 6/2
r = 3

Then, we find the centerpoint by finding the midpoint of both points, since the center of a diameter is the center of the circle. Let centerpoint be (h,k). The formula would be

h = (x1 +x2)/2 = (-2+4)/2 = 1
k = (y1 + y2)/2 = (2+2)/2 = 2

Now that we know all parameters, we substitute this to the standard equation for a circle:

(x - h)² + (y - k)² = r²
(x-1)² + (y - 2)² = 3²

The equation of the circle would be (x-1)² + (y - 2)² = 9