Consider the hyperbola 
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 
SPS 1 = 
, with 
. 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 
be the distance of P from the straight line SP 1 , and 
= S 1 P. Then the greatest integer less than or equal to 
is
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