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 (9secθ,7tanθ) then ON=9secθEquation of the tangent at P is x9secθ−y7tanθ=1 which meets the transverse axis at (9cosθ,0)⇒OT=9cosθThen ON.OT=9secθ×9cosθ=81.
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