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Question

P is a point on the hyperbola x24y29=1, N is the foot of perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of hyperbola, then the value of OT×ONis

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Solution


Let P(x1,y1)
N(x1,0)ON=x1 units
Equation of tangent at P is
T=0xx14yy19=1
The point of intersection of this tangent on the transverse axis (y=0) is
T=(4x1,0)OT=4x1 unitsOT×ON=4x1×x1=4

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