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Let P be a point on the hyperbola $\frac{x^{2}}{81} - \frac{y^{2}}{49} = 1$ .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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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.

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