Question

Show that the equation of the circle passing through (1,1) and the points of intersection

Answer 1

The equation of circle passing through point  of intersection of two circles is

(x2+y2+13x-3y)+k (2x2+2y2+4x-7y-25)=0 ....(I)

Now circle passes through (1,1) so

1+1+13-3+k(2+2+4-7-25)=0

So 12+k(-24) =0 or k =-1/2

Substituting k =-1/2 in (I) required equation can be obtained.