Question

The angle between the asymptotes to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ is

• A. $\pi -2{\tan }^{-1}\left(\frac{3}{4}\right)$
• B. $\pi -2{\tan }^{-1}\left(\frac{4}{3}\right)$
• C. $2{\tan }^{-1}\left(\frac{3}{4}\right)$
• D. $2{\tan }^{-1}\left(\frac{4}{3}\right)$

Answer 1

Answer: (C)

$2{\tan }^{-1}\left(\frac{3}{4}\right)$

Fact: Angle between asymptotes of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $2{\tan }^{-1}\left(\frac{b}{a}\right)$

Hence angle between the asymptotes to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ is $2{\tan }^{-1}\left(\frac{3}{4}\right)$