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Hyperbola in conic sections

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.


Let the coordinate of P be (9secθ,7tanθ)  then ON=9secθ

Equation of the tangent at P is x9secθy7tanθ=1 which meets the transverse axis at (9cosθ,0)OT=9cosθ

Then ON.OT=9secθ×9cosθ=81.

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