$P=\sqrt{\frac{y-a}{y+1}}$
$y\neq -1$

$a=-yP^{2}+y-P^{2}$
$y\neq -1\text{ and }\left(P=0\text{ or }arg(P)<\pi \right)$

$P=\sqrt{\frac{y-a}{y+1}}$
$\left(y=a\text{ and }a\neq -1\right)\text{ or }\left(y\leq a\text{ and }y<-1\right)\text{ or }\left(y\geq a\text{ and }y>-1\right)$

$a=-yP^{2}+y-P^{2}$
$P\geq 0\text{ and }y\neq -1$