Value of $\lambda$ for two tangents intersect at origin

Question

I am not getting any idea . Can anybody provide me a hint

Answer 1

HINT:

$$x^2+y^2+8x+8y+16+\lambda(x+y+12)=0$$ represents the equation of the circle passing through the intersections$A,B$ of $$x+y+12=0$$ and $$x^2+y^2+8x+8y+16=0$$