$$x^{2}+y^{2}-10x+6y-15=0$$
$x=\sqrt{\left(4-y\right)\left(y+10\right)}+5$
$x=-\sqrt{\left(4-y\right)\left(y+10\right)}+5$
$y=\sqrt{-\left(x-12\right)\left(x+2\right)}-3$
$y=-\sqrt{-\left(x-12\right)\left(x+2\right)}-3$
$x=\sqrt{\left(4-y\right)\left(y+10\right)}+5$
$x=-\sqrt{\left(4-y\right)\left(y+10\right)}+5\text{, }y\geq -10\text{ and }y\leq 4$
$y=\sqrt{\left(12-x\right)\left(x+2\right)}-3$
$y=-\sqrt{\left(12-x\right)\left(x+2\right)}-3\text{, }x\geq -2\text{ and }x\leq 12$