Hyperbola Focus Latus Rectum (Jee Mains)

Hyperbola

Medium

Hyperbola Focus Latus Rectum

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

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