It is given that the points (0, 2a) and (2b , 0) are the end points of a diameter.

The center of the circle is the mid point between the points (0, 2a) and (2b , 0).

The center is (b , a)

The radius of the circle is the distance between the center and any of the given points.

radius = sqrt [( b^2 + a^2)]

The equation of the circle with center ( b, a) and radius sqrt [( b^2 + a^2)] is:

(x - b)^2 + ( y - a)^2 = b^2 + a^2

=> x^2 + b^2 - 2xb + y^2 + a^2 - 2ya = b^2 + a^2

=> x^2 - 2xb + y^2 - 2ya = 0

=> x^2 + y^2 - 2xb - 2ya = 0

The required equation of the circle is x^2 + y^2 - 2xb - 2ya = 0