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Q.

Let P be a point on the hyperbola x281−y249=1 .The tangent at P meets the transverse axis at T, N is the foot of the perpendicular from P to the transverse axis. If O is the origin, then ON.OT is equal to.

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a

81

b

49

c

-81

d

-49

answer is A.

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Detailed Solution

Let the coordinate of P be (9sec⁡θ,7tan⁡θ)  then ON=9sec⁡θEquation of the tangent at P is x9sec⁡θ−y7tan⁡θ=1 which meets the transverse axis at (9cos⁡θ,0)⇒OT=9cos⁡θThen ON.OT=9sec⁡θ×9cos⁡θ=81.
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