Consider the hyperbola x^2/a^2-y^2/b^2=1 having one of its focus at P (-3,0). If the latus ractum through its other focus subtends a right angle at P…

Consider the hyperbola $\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ having one of its focus at $\displaystyle \mathrm{P}(-3,0)$. If the latus ractum through its other focus subtends a right angle at P and $\displaystyle a^2 b^2=\alpha \sqrt{2}-\beta, \alpha, \beta \in \mathbb{N}$, then $\displaystyle \alpha+\beta$ is $\displaystyle \_\_\_\_$.