Let $a,b,c$ be positive numbers. The following system of equations in $x,y$ and $z . \large\frac{x^2}{a^2} +\frac{y^2}{b^2} -\frac{z^2}{c^2}$$=1;\large\frac{x^2}{a^2} -\frac{y^2}{b^2} +\frac{z^2}{c^2}$$=1;\large\frac{-x^2}{a^2} +\frac{y^2}{b^2} + \frac{z^2}{c^2}$$=1$;

Question

$\begin{array}{1 1} no\;solution \\ unique\;solution \\ infinitely\;many\;solutions \\ finitely\;many \;solutions \end{array}$