$x=\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{C}$
$x=-\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{C}$
$x=\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{C}$
$x=-\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{C}$

$x=-\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \begin{bmatrix}-\frac{\sqrt{2}|b|}{|c|},\frac{\sqrt{2}|b|}{|c|}\end{bmatrix}\text{; }x=-\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\geq -\frac{\sqrt{2}|b|}{|c|}\text{; }x=-\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{R}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \begin{bmatrix}-\frac{\sqrt{2}|b|}{|c|},\frac{\sqrt{2}|b|}{|c|}\end{bmatrix}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\geq -\frac{\sqrt{2}|b|}{|c|}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=-\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{R}\text{; }x=-\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \begin{bmatrix}-\frac{\sqrt{2}|b|}{|c|},\frac{\sqrt{2}|b|}{|c|}\end{bmatrix}\text{; }x=-\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\geq -\frac{\sqrt{2}|b|}{|c|}\text{; }x=-\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{R}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \begin{bmatrix}-\frac{\sqrt{2}|b|}{|c|},\frac{\sqrt{2}|b|}{|c|}\end{bmatrix}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\geq -\frac{\sqrt{2}|b|}{|c|}\text{; }x=\sqrt{2a^{2}-b^{2}}\text{, }y=\sqrt{2b^{2}-\left(cz\right)^{2}}\text{, }z\in \mathrm{R}\text{, }|a|\geq \frac{\sqrt{2}|b|}{2}\text{ and }c\neq 0$