P(−1, 2) and Q(7, 8)
The midpoint of PQ will be the center of the ciricle
So
( [ -1 + 7 ] /2 , [ 8 + 2 ] /2 ) = [ 6/2 , 10/2) = (3 , 5) = (h, k)
And the distance from this point to either P or Q is the radius, r
And we can find r^2 as
(7 -3)^2 + ( 8 - 5)^2 = r^2
4^2 + 3^2 = r^2
16 + 9 = r^2
25 = r^2
So....the equation of the circle is
(x - h)^2 + (y - k)^2 = r^2
( x - 3)^2 + (y - 5)^2 = 25