Let the circle passes through the origin O.
Given : OA = a and OB = b
$:.""A-=(a,0)andB-=(0,b)$
$becauseangle(AOB=90^(@)$
$:.$ AB is the diameter of circle.
Equation of the circle , the end points of whose diameter are $(x(1),y(1))and(x(2),y(2))$ is
$(x-x(1))(x-x(2))+(y-y(2))(y-y(2))=0$.
$:.$ Equation of circle, the coordinates of the end points of whose diameter are (A,0) and (0,b) is
(x-a)(x-0)+(y-0)(y-b)=0
$rArr""x^(2)+y^(2)-ax-by=0$
But the intercepts can be any direction.
So, four circles are possible whose equations are.
$x^(2)+y^(2)pmaxpmby=0$
