Solve 1/a^2+1/b^2=1/h^2

$$\frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = \frac { 1 } { h ^ { 2 } }$$

Solve for a (complex solution)

$$a=-i\left(h^{2}-b^{2}\right)^{-\frac{1}{2}}bh$$

$$a=i\left(h^{2}-b^{2}\right)^{-\frac{1}{2}}bh\text{, }b\neq 0\text{ and }h\neq 0\text{ and }b\neq -h\text{ and }b\neq h$$

Solve for b (complex solution)

$$b=-i\left(h^{2}-a^{2}\right)^{-\frac{1}{2}}ah$$

$$b=i\left(h^{2}-a^{2}\right)^{-\frac{1}{2}}ah\text{, }a\neq 0\text{ and }h\neq 0\text{ and }a\neq -h\text{ and }a\neq h$$

Solve for a

$$a=\sqrt{-\frac{1}{h^{2}-b^{2}}}bh$$

$$a=-\sqrt{-\frac{1}{h^{2}-b^{2}}}bh\text{, }h\neq 0\text{ and }b\neq 0\text{ and }|b|>|h|$$

Solve for b

$$b=\sqrt{-\frac{1}{h^{2}-a^{2}}}ah$$

$$b=-\sqrt{-\frac{1}{h^{2}-a^{2}}}ah\text{, }h\neq 0\text{ and }a\neq 0\text{ and }|a|>|h|$$