The point $C$ moves along the hyperbolic curve which is given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$.
The distances $d_{0}$ and $d_{1}$ in from $A$ to $C$ and $B$ to $C$ respectively.
How to find the point $C$ such that minimize the total length $d_{0}+d_{1}$?