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 \(\frac{\beta\delta}{9}sin\frac{\alpha}{2}\) is _____.
