Need some help. how do you find the equation of a circle with endpoints of the diameter at (-1,1) and (7,9)?

1 Answer
May 11, 2018

(x-3)^2 + (y-5)^2 = 32

Explanation:

Urgent!

The center is the midpoint of the diameter:

(a,b) = ({-1 + 7}/2, {1+9}/2 ) = (3,5)

The squared radius is the squared distance from the center to either endpoint:

r^2 = (3 - -1)^2 + (5-1)^2 = 32

The general equation for a circle with center (a,b) and radius r is

(x-a)^2 + (y-b)^2 = r^2

(x-3)^2 + (y-5)^2 = 32