$x=-\sqrt{y^{2}-8}$
$x=\sqrt{y^{2}-8}$

$x=\sqrt{y^{2}-8}$
$x=-\sqrt{y^{2}-8}\text{, }|y|\geq 2\sqrt{2}$

$y=\sqrt{x^{2}+8}$
$y=-\sqrt{x^{2}+8}$