Q. The angle between the pair of straight lines $y^{2}\sin^{2}\theta - xy\sin^{2}\theta + x^{2}\left( \cos^{2}\theta - 1 \right) = 0$ is
A) $\pi/3$
B) $\pi/4$
C) $\pi/6$
D) $\pi/2$
Explanation
(d)
The given equation is
$x^{2}\left( \cos^{2}\theta - 1 \right) - xy\sin^{2}\theta + y^{2}\sin^{2}\theta = 0$
$Here,\ a = \cos^{2}\theta - 1,\ h = - \frac{1}{2}\sin^{2}\theta,\ b = \sin^{2}\theta$
$a + b = \cos^{2}\theta + \sin^{2}\theta - 1 = 1 - 1 = 0$
$\therefore The\ angle\ between\ the\ pair\ of\ straight\ lines\ is\ \frac{\pi}{2}$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.