Question

The angle between two asymptotes of the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$ is

• A. ${\tan }^{-1}\frac{4}{5}$
• B. $2{\tan }^{-1}\frac{4}{5}$
• C. $2{\tan }^{-1}\frac{5}{4}$
• D. $\pi -2{\tan }^{-1}\frac{4}{5}$

Answer 1

The correct option is B $2{\tan }^{-1}\frac{4}{5}$

We know that angle between asymptotes of hyperbola

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is, $\theta =2{\tan }^{-1}\left(\frac{b}{a}\right)$

Here $a=5$ and $b=4$

Hence required angle is, $\theta =2{\tan }^{-1}\left(\frac{4}{5}\right)$