Circle

since line passes through fourth quadrent so center of circle must be in fourth quad. so center of circle is (h ,-h)

 and radius is h.

the eqn. of circle touches axes is (x - h )²  + (y + h)² = h²

since point (h ,-h) lie on line x - 2y = 3 so  h - 2(-h) = 3  ===>h =1

so eqn of circle is (x - 1)² +(y +1)² = 1