Question

$$x=\frac{\sqrt{a}}{y}+b$$

Solve for a

$a=\left(y\left(x-b\right)\right)^{2}$
$\left(y>0\text{ or }x\leq b\right)\text{ and }\left(y<0\text{ or }x\geq b\right)\text{ and }y\neq 0$

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Solve for b

$b=x-\frac{\sqrt{a}}{y}$
$a\geq 0\text{ and }y\neq 0$

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