Find the equation of the circle whose endpoints of the diameter are (5, 8) and (8, 10).

Answer 1

The radius is half the length of the diameter.

length of diameter = sqrt((10-8)^2 + (8-5)^2) = sqrt(16 + 9) = 5

radius = 2.5

The center is the midpoint of the endpoints of the diameter.

(5+8/2,8+10/2) = (6.5,9)

equation of circle = (x-h)^2 + (y-k)^2 = r^2

where (h,k) = (6.5,9)

and r^2 = 2.5*2.5 = 6.25