P is a point on hyperbola frac{{{x^2}}}{{{a^2}}} - frac{{{y^2}}}{{{b^2}}} = 1, N is foot of p

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10-2. Parabola, Ellipse, Hyperbola

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$P$ is a point on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}}$ $= 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, the $OT. ON$ is equal to :

A

$e^2$

B

$a^2$

C

$b^2$

D

$b^2/a^2$

Solution

$OT = a cos \theta $ ; $N = a sec \theta$ $ \Rightarrow $ $OT . ON = a^2$

Standard 11

Mathematics

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