Let $a,b,c$ be the real numbers. Then the following system of equations in $x,y$ and $z$: $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$, $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$, $\large\frac{-x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ has

Question

$\begin{array}{1 1}(a)\;No \;solution&(b)\;unique\;solution\\(c)\;infinitely\;many\;solutions&(d)\;finitely\;many\;solutions\end{array}$