Solve x^2/10+left(x+mright)^2/y=1

$$\frac{ { x }^{ 2 } }{ 10 } + \frac{ { \left(x+m \right) }^{ 2 } }{ y } = 1$$

Solve for m (complex solution)

$$m=\frac{\sqrt{100y-10yx^{2}}}{10}-x$$

$$m=-\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{, }y\neq 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{10y\left(y-m^{2}+10\right)}-10m}{y+10}\text{; }x=-\frac{\sqrt{10}\left(\sqrt{y\left(y-m^{2}+10\right)}+\sqrt{10}m\right)}{y+10}\text{, }&y\neq -10\text{ and }y\neq 0\\x=\frac{-m^{2}-10}{2m}\text{, }&m\neq 0\text{ and }y=-10\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{; }m=\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{, }&|x|\geq \sqrt{10}\text{ and }y<0\\m=\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{, }&\left(y>0\text{ and }|x|\leq \sqrt{10}\right)\text{ or }\left(|x|=\sqrt{10}\text{ and }y\neq 0\right)\\m=-\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{, }&|x|=\sqrt{10}\text{ and }y\neq 0\\m=-\frac{\sqrt{100y-10yx^{2}}}{10}-x\text{, }&y>0\text{ and }|x|\leq \sqrt{10}\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{10y\left(y-m^{2}+10\right)}-10m}{y+10}\text{; }x=-\frac{\sqrt{10}\left(\sqrt{y\left(y-m^{2}+10\right)}+\sqrt{10}m\right)}{y+10}\text{, }&y\neq -10\text{ and }\left(y<0\text{ or }|m|\leq \sqrt{y+10}\right)\text{ and }y\neq 0\text{ and }\left(y<-10\text{ or }y>0\text{ or }|m|\geq \sqrt{y+10}\right)\\x=\frac{-m^{2}-10}{2m}\text{, }&m\neq 0\text{ and }y=-10\end{matrix}\right.$$