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