The equation of the circle passing through intersection of line x+y+1=0 and circle x2+y2+x+3y=0 is x2+y2+x+3y+λ(x+y+1)=0 x2+y2+(1+λ)x+(3+λ)y+λ=0 Let the intersection points of tangents A and B is (h,k). Then xh+yk+
x+h
2
+
3y+3k
2
=0 (2h+1)x+(2k+3)y+h+3k=0 since x+y+1=0 is identical to the above line.
2h+1
1
=
2k+3
1
=
h+3k
1
h=2 and k=1 This implies (2,1) is the point of the circle. Then, x2+y2+(1+λ)2+(3+λ)+λ=0 λ=−