The equation of a circle passing through points of intersection of the circles x2+y2+13x−3y=0 and 2x2+2y2+4x−7y−25=0 and point (1, 1) is
4x2+4y2+30x−13y−25=0
Required equation is
(x2+y2+13x−3y)+λ(2x2+2y2+4x−7y−25)=0
which passes through (1, 1), so λ=12.
Hence required equation is
4x2+4y2+30x−13y−25=0.