If (5, 4) and (7,2) are the endpoints of a diameter of a circle, what is the equation of the circle?

  (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

a is the right answer

0,0

step-by-step explanation: