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Let P be a point on the hyperbola x281y249=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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By Expert Faculty of Sri Chaitanya
a
81
b
49
c
-81
d
-49

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detailed solution

Correct option is A

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.
ctaimg

ctaimg

Similar Questions

Statement-1: The locus of the point of intersection of the tangents that are at right angles to the hyperbola x236-y216=1 is the circle x2+y2=52

Statement-2: Perpendicular tangents to the hyperbola x2a2-y2b2=1 interest on the director circle  x2+y2=a2-b2a2>b2 of the hyperbola.

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