Q. The angle between the two asymptotes of the hyperbola $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1$ is
A) $\pi - 2\tan^{- 1}\left( \frac{3}{4} \right)$
B) $\pi - 2\tan^{- 1}\left( \frac{3}{2} \right)$
C) $2\tan^{- 1}\left( \frac{3}{4} \right)$
D) $\pi - 2\tan^{- 1}\left( \frac{4}{3} \right)$
Explanation
(c)
We know that angle between two asymptotes of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is $2\tan^{- 1}{\left( \frac{b}{a} \right).}$
Equation of given hyperbola is $\frac{x^{2}}{16} - \frac{y^{2}}{9} = 1.$
Here, $a = 4\$ and $b = 3$
$\therefore\$ Required angle $= 2\tan^{- 1}\left( \frac{3}{4} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.