Equation of the circle passing through the intersection of ellipses x2a2+y2b2=1 and x2b2+y2a2=1 is

Given equations of ellipse arex2a2+y2b2=1 and x2b2+y2a2=1 The point of the intersection of these ellipse are±aba2+b2,±aba2+b2Paba2+b2,aba2+b2The distance between OP= r=aba2+b2−02+aba2+b2−02=aba2+b22∴ Equation of circle is x2+y4=r2⇒x2+y2=2a2b2a2+b2