Solve left(left|xright|-8right)^2+left(left|yright|-15right)^2=81

$${ \left( \left| x \right| -8 \right) }^{ 2 } + { \left( \left| y \right| -15 \right) }^{ 2 } =81$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{-\left(y+6\right)\left(y+24\right)}+8\text{; }x=-\sqrt{-\left(y+6\right)\left(y+24\right)}-8\text{, }&y\geq -24\text{ and }y\leq -6\\x=-\sqrt{-\left(y+6\right)\left(y+24\right)}+8\text{; }x=\sqrt{-\left(y+6\right)\left(y+24\right)}-8\text{, }&\left(y\geq \sqrt{17}-15\text{ and }y\leq -6\right)\text{ or }\left(y\geq -24\text{ and }y\leq -\sqrt{17}-15\right)\\x=\sqrt{\left(24-y\right)\left(y-6\right)}+8\text{; }x=-\sqrt{\left(24-y\right)\left(y-6\right)}-8\text{, }&y\geq 6\text{ and }y\leq 24\\x=-\sqrt{\left(24-y\right)\left(y-6\right)}+8\text{; }x=\sqrt{\left(24-y\right)\left(y-6\right)}-8\text{, }&\left(y\geq \sqrt{17}+15\text{ and }y\leq 24\right)\text{ or }\left(y\geq 6\text{ and }y\leq 15-\sqrt{17}\right)\end{matrix}\right.$$

Solve for y

$$y=\sqrt{-x^{2}+16|x|+17}+15$$

$$y=-\sqrt{-x^{2}+16|x|+17}-15$$

$$y=\sqrt{-x^{2}+16|x|+17}-15$$

$$y=-\sqrt{-x^{2}+16|x|+17}+15\text{, }|x|\leq 17$$