Find these equation of the pair of straight lines through the origin which please through the intersection of these curves: $x^2+y^2-2x-2y-2=0$ and $x^2+y^2-6x-6y+14=0$
The equation of the family of curves passing through the intersection of the given two curves will be $x^2+y^2-2x-2y-2+\lambda (x^2+y^2-6x-6y+14)=0$
Now, for this curve to be a pair of straight lines passing through the origin, should be a homogenous second degree equation.
So we have to choose a suitable $\lambda$, so that there coefficient of $x$ and $y$ and also the constant term is $0$. But I am unable to do that. Please help