If angle between asymptotes of hyperbola frac{{{x^2}}}{{{a^2}}} - frac{{{y^2}}}{3} = 4 is&nbsp

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10-2. Parabola, Ellipse, Hyperbola

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If angle between asymptotes of hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{3} = 4$ is $\frac{\pi }{3}$, then its conjugate hyperbola is

A

$\frac{{{y^2}}}{{19}} - \frac{{{x^2}}}{9} = 1$

B

$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{{25}} = 1$

C

$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{{36}} = 1$

D

$\frac{{{y^2}}}{{12}} - \frac{{{x^2}}}{{4}} = 1$

Solution

$2 \tan ^{-1} \frac{b}{a}=\frac{\pi}{3},$ where $b=2 \sqrt{3}$

$\Rightarrow \quad \frac{b}{a}=\frac{1}{\sqrt{3}}$

$\Rightarrow \quad \alpha=6$

conjugate hyperbola is $\frac{x^{2}}{36}-\frac{y^{2}}{12}=-1$

Standard 11

Mathematics

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