Q. The angle between the lines $x^{2} + 4xy + y^{2} = 0$ is

A) $60{^\circ}$
B) $15{^\circ}$
C) $30{^\circ}$
D) $45{^\circ}$
Explanation

(a)
On comparing the given equation with the standard form of equation, we get $a = 1,\ h = 2$ and $b = 1$
Let $\theta$ is the angle between them, then
$\tan\theta = \frac{2\sqrt{h^{2} - ab}}{a + b}$
$\therefore\tan\theta = \frac{2\sqrt{2^{2} - 1}}{1 + 1} = \frac{2\sqrt{4 - 1}}{2} = \sqrt{3}$
$\Rightarrow \ \theta = \tan^{- 1}\left( \sqrt{3} \right) = 60{^\circ}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.