$x=\sqrt{-2y^{2}-8y-4}+1$
$x=-\sqrt{-2y^{2}-8y-4}+1$

$y=\frac{\sqrt{6+4x-2x^{2}}}{2}-2$
$y=-\frac{\sqrt{6+4x-2x^{2}}}{2}-2$

$x=\sqrt{-2y^{2}-8y-4}+1$
$x=-\sqrt{-2y^{2}-8y-4}+1\text{, }y\geq -\sqrt{2}-2\text{ and }y\leq \sqrt{2}-2$

$y=\frac{\sqrt{6+4x-2x^{2}}}{2}-2$
$y=-\frac{\sqrt{6+4x-2x^{2}}}{2}-2\text{, }x\geq -1\text{ and }x\leq 3$