Q. The angle between the asymptotes of the hyperbola $x^{2} + 2xy - 3y^{2} + x + 7y + 9 = 0$ is
A) $\tan^{- 1}( \pm 2)$
B) $\tan^{- 1}\left( \pm \sqrt{3} \right)$
C) $\tan^{- 1}\left( \frac{1}{\sqrt{3}} \right)$
D) $\tan^{- 1}\left( \frac{1}{2} \right)$
Explanation
(a)
Equation of asymptotes of the hyperbola are
$x^{2} + 2xy - 3y^{2} = 0$
The angle between asymptotes is
$\theta = \tan^{- 1}\left( \frac{1 - 1( - 3)}{1 - 3} \right)$
$= \tan^{- 1}{\left( \frac{1 + 3}{- 2} \right) = \tan^{- 1}{( \pm 2)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.