$$x^{2}+y^{2}-4x+6y-3=0$$
$x=\sqrt{\left(1-y\right)\left(y+7\right)}+2$
$x=-\sqrt{\left(1-y\right)\left(y+7\right)}+2$
$y=\sqrt{-\left(x-6\right)\left(x+2\right)}-3$
$y=-\sqrt{-\left(x-6\right)\left(x+2\right)}-3$
$x=\sqrt{\left(1-y\right)\left(y+7\right)}+2$
$x=-\sqrt{\left(1-y\right)\left(y+7\right)}+2\text{, }y\geq -7\text{ and }y\leq 1$
$y=\sqrt{\left(6-x\right)\left(x+2\right)}-3$
$y=-\sqrt{\left(6-x\right)\left(x+2\right)}-3\text{, }x\geq -2\text{ and }x\leq 6$