Question

The diameter of a circle has endpoints whose coordinates are R(-2, 2) and S(4, 2). Find the equation of the circle.

Answer 1

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