Answer:
(x -6)^2 +(y -3)^2 = 2
Step-by-step explanation:
The midpoint (C) is the center of the circle:
C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)
A circle with center (h, k) that goes through point (a, b) can be written as ...
(x -h)^2 +(y -k) ^2 = (a -h)^2 +(b -k)^2
Using the values for this problem, we get ...
(x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2
(x -6)^2 +(y -3)^2 = 2
