Mathematics - Hyperbola Question with Solution | TestHub

Consider the hyperbola$\frac{x^2}{100}-\frac{y^2}{64}=1$with foci at$S$and$S_1$, where$S$lies on the positive$x$-axis. Let$P$be a point on the hyperbola, in the first quadrant. Let$\angle SP{S}_1=\alpha$, with$\alpha <\frac{\pi }{2}$. The straight line passing through the point$S$and having the same slope as that of the tangent at$P$to the hyperbola, intersects the straight line$S_{1}P$at$P_1$. Let$\delta$be the distance of$P$from the straight line$S{P}_1$, and$\beta =S_{1}P$. Then the greatest integer less than or equal to$\frac{\beta \delta }{9}\sin \frac{\alpha }{2}$is _____ .