Solve 0=sqrt{a^2-h^2/c^2}+sqrt{frac{b^2-{h}^2}{{c}^2}}

$$0 = \sqrt{ \frac{ { a }^{ 2 } - { h }^{ 2 } }{ { c }^{ 2 } } } + \sqrt{ \frac{ { b }^{ 2 } - { h }^{ 2 } }{ { c }^{ 2 } } }$$

Solve for a (complex solution)

$$a=-b$$

$$a=b\text{, }\left(h=-b\text{ or }h=b\right)\text{ and }c\neq 0$$

Solve for b (complex solution)

$$b=-a$$

$$b=a\text{, }\left(a=-h\text{ or }a=h\right)\text{ and }c\neq 0$$

Solve for a

$$a=-b$$

$$a=b\text{, }c\neq 0\text{ and }\left(h\geq -|b|\text{ or }b=|h|\right)\text{ and }\left(b=|h|\text{ or }|b|=|h|\text{ or }h\geq b\right)\text{ and }|h|=|b|$$

Solve for b

$$b=-a$$

$$b=a\text{, }\left(c\neq 0\text{ and }h\leq 0\text{ and }a=h\right)\text{ or }\left(c\neq 0\text{ and }h=-a\text{ and }a\leq 0\right)\text{ or }\left(h=a\text{ and }c\neq 0\text{ and }a\geq 0\right)\text{ or }\left(c\neq 0\text{ and }|a|=|h|\right)\text{ or }\left(c\neq 0\text{ and }h=|a|\right)$$