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Standard XII

Mathematics

Parabola

P is a point ...

Question

P is a point on the hyperbola $\frac{x^{2}}{3} - \frac{y^{2}}{5} = 1$ , N is the foot of the 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 the hyperbola, then find the value of OT . ON .

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Solution

The correct option is D $3$
$O T = a c o s θ$ ; $O N = a s e c θ$ $\Rightarrow O T . O N = a^{2}$

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P is a point on the hyperbola x23−y25=1, N is the foot of the 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 the hyperbola, then find the value of OT . ON .

The correct option is D 3OT=acosθ ; ON=asecθ ⇒OT.ON=a2

P is a point on the hyperbola $\frac{x^{2}}{3} - \frac{y^{2}}{5} = 1$ , N is the foot of the 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 the hyperbola, then find the value of OT . ON .

The correct option is D $3$
$O T = a c o s θ$ ; $O N = a s e c θ$ $\Rightarrow O T . O N = a^{2}$