Question

The angle between the asymptotes of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

• A. $2{\tan }^{-1}\left(\frac{b}{a}\right)$
• B. ${\tan }^{-1}\left(\frac{a}{b}\right)$
• C. $2{\tan }^{-1}\left(\frac{a}{b}\right)$
• D. ${\tan }^{-1}\left(\frac{b}{a}\right)$

Answer 1

Answer: (A)

$2{\tan }^{-1}\left(\frac{b}{a}\right)$

Asymptotes of $\frac{x^2}{a^2}-\frac{-y^2}{b^2}=1$ is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=0$

$\Rightarrow \tan \theta =\frac{b}{a}$

$\therefore \theta ={\tan }^{-1}\left(\frac{h}{a}\right)$

$\therefore$ Ange between two asymptotes $=2\theta$

$=2{\tan }^{-1}\left(\frac{b}{a}\right)$