JEE Advanced 2022 Paper 2

Consider the hyperbola
‌

x2

100

−‌

y2

64

=1
with foci at S and S1, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let ∠SPS1=α, with α<‌

π

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 S1P at P1. Let δ be the distance of P from the straight line SP1, and β=S1P. Then the greatest integer less than or equal to ‌

βδ

9

‌sin‌

α

2

is____