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Consider the hyperbola x 2 100 - 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 ∠ S P S 1 = 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 S 1 P at P 1 . Let δ be the distance of P f

Correct answer

0

Step-by-step solution

Plotting the diagram of the given value we have, We know that product of distances of any tangent from two foci = b 2 So, δ × β sin α 2 = b 2 ⇒ β δ sin α 2 9 = b 2 9 = 64 9 Now finding the greatest integer less than or equal to β δ sin α 2 9 which will be 7

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