Branch 1: △AOB is a right triangle, the center of the circumscribed circle of the right triangle is at the midpoint of the hypotenuse, and the radius is half of the hypotenuse.

The midpoint coordinate of AB is (2,3/2), and r=5/2 (according to Pythagorean theorem, the hypotenuse can be found to be 5).

So (x-2) 2+(y-3/2) 2 = (5/2) 2.

(x-2)^2+(y-3/2)^2=25/4

This is the standard equation. If you need a general equation, do it yourself.