Let S1≡x2+y2+13x−3y=0 and S2≡2x2+2y2+4x−7y−25=0 Equation of circle passing through point of intersection of S1 and S2 is given by S1+λS2=0 (x2+y2+13x−3y)+λ(2x2+2y2 +4x−7y−25)=0 . . . (i) This circle is passing through (1,1). ∴[12+12+13(1)−3(1)]+λ[2(1)22(1)2 +4(1)−7(1)−25]=0 From Eq. (i), we get ⇒λ=1∕2 4x2+4y2+30x−13y−25=0