Solve x^2-xy+y^2leq13

$$x ^ { 2 } - x y + y ^ { 2 } \leq 13$$

Solve for x

$$\left\{\begin{matrix}x\in \begin{bmatrix}\frac{-\sqrt{52-3y^{2}}+y}{2},\frac{\sqrt{52-3y^{2}}+y}{2}\end{bmatrix}\text{, }&|y|<\frac{2\sqrt{39}}{3}\\x=\frac{\sqrt{39}}{3}\approx 2.081665999\text{, }&y=\frac{2\sqrt{39}}{3}\text{ or }\left(y\geq -\frac{\sqrt{39}}{3}\text{ and }|y|\leq \frac{2\sqrt{39}}{3}\right)\\x=-\frac{\sqrt{39}}{3}\approx -2.081665999\text{, }&\left(|y|\leq \frac{2\sqrt{39}}{3}\text{ and }y\leq \frac{\sqrt{39}}{3}\right)\text{ or }y=-\frac{2\sqrt{39}}{3}\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y\in \begin{bmatrix}\frac{-\sqrt{52-3x^{2}}+x}{2},\frac{\sqrt{52-3x^{2}}+x}{2}\end{bmatrix}\text{, }&|x|<\frac{2\sqrt{39}}{3}\\y=\frac{\sqrt{39}}{3}\text{, }&x=\frac{2\sqrt{39}}{3}\text{ or }\left(x\geq -\frac{\sqrt{39}}{3}\text{ and }|x|\leq \frac{2\sqrt{39}}{3}\right)\\y=-\frac{\sqrt{39}}{3}\text{, }&\left(|x|\leq \frac{2\sqrt{39}}{3}\text{ and }x\leq \frac{\sqrt{39}}{3}\right)\text{ or }x=-\frac{2\sqrt{39}}{3}\end{matrix}\right.$$