The equation of the circle on the common chord of the circles(x−a)2+y2=a2 and  x2+(y+b)2=b2 as diameter is ,

The equation of the common chord of the circles (x−a)2+y2=a2 and x2+(y+b)2=b2 ax+by=0The equation of the required circle is (x−a)2+y2−a2+λ(ax+by)=0⇒x2+y2+x(aλ−2a)+λby=0               (i)Since (i) is a diameter of circle (ii).  ∴a−(aλ−2a)2+b−λ,b2=0⇒λ=2a2a2+b2Putting the value of A in (ii), the equation of the required circle is a2+b2x2+y2=2ab(bx−ay)