A variable generator meets two generators of the system through the extremities $B$ and $B'$ of the principal elliptic section of the hyperboloid $$\frac{x^2}{a^2} + \frac{y^2}{b^2} -z^2c^2=1$$ in $P$ and $P'$. Prove $BP.B'P'=a^2+c^2$.
I found the intersection point of $\lambda$ and $\mu$ system of generators. Not able to proceed from there. Please help.