Equation of tangent at point (asec θ ,btan θ ) of conic frac{{{x^2}}}{{{a^2}}} - frac{{{y^2}}}{{{b

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10-2. Parabola, Ellipse, Hyperbola

easy

The equation of the tangent at the point $(a\sec \theta ,\;b\tan \theta )$ of the conic $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$, is

A

$x{\sec ^2}\theta - y{\tan ^2}\theta = 1$

B

$\frac{x}{a}\sec \theta - \frac{y}{b}\tan \theta = 1$

C

$\frac{{x + a\sec \theta }}{{{a^2}}} - \frac{{y + b\tan \theta }}{{{b^2}}} = 1$

D

None of these

Solution

(b) $\frac{{x(a\sec \theta )}}{{{a^2}}} – \frac{{y(b\tan \theta )}}{{{b^2}}} = 1$

==> $\frac{x}{a}\sec \theta – \frac{y}{b}\tan \theta = 1$.

Standard 11

Mathematics

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