Solve x^2/a^2-y^2/b^2=2

$$\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 2$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-i\left(-y^{2}-2b^{2}\right)^{-\frac{1}{2}}bx\text{; }a=i\left(-y^{2}-2b^{2}\right)^{-\frac{1}{2}}bx\text{, }&b\neq 0\text{ and }x\neq 0\text{ and }y\neq -\sqrt{2}ib\text{ and }y\neq \sqrt{2}ib\\a\neq 0\text{, }&\left(y=-\sqrt{2}ib\text{ or }y=\sqrt{2}ib\right)\text{ and }x=0\text{ and }b\neq 0\end{matrix}\right.$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-i\left(2a^{2}-x^{2}\right)^{-\frac{1}{2}}ay\text{; }b=i\left(2a^{2}-x^{2}\right)^{-\frac{1}{2}}ay\text{, }&a\neq 0\text{ and }y\neq 0\text{ and }x\neq -\sqrt{2}a\text{ and }x\neq \sqrt{2}a\\b\neq 0\text{, }&\left(x=-\sqrt{2}a\text{ or }x=\sqrt{2}a\right)\text{ and }y=0\text{ and }a\neq 0\end{matrix}\right.$$

Solve for a

$$a=\frac{bx}{\sqrt{y^{2}+2b^{2}}}$$

$$a=-\frac{bx}{\sqrt{y^{2}+2b^{2}}}\text{, }b\neq 0\text{ and }x\neq 0$$

Solve for b

$$\left\{\begin{matrix}b=\sqrt{-\frac{1}{2a^{2}-x^{2}}}ay\text{; }b=-\sqrt{-\frac{1}{2a^{2}-x^{2}}}ay\text{, }&a\neq 0\text{ and }y\neq 0\text{ and }|x|>\sqrt{2}|a|\\b\neq 0\text{, }&y=0\text{ and }|x|=\sqrt{2}|a|\text{ and }a\neq 0\end{matrix}\right.$$