Q. If pairs straight lines $x^{2} - 2pxy - y^{2} = 0$ and $x^{2} - 2qxy - y^{2} = 0$ be such that each pair bisects the angle between the other pair, then
A) $pq = 1$
B) $pq = - 1$
C) $pq = 2$
D) $pq = - 2$
Explanation
(b)
Equation of bisector between the lines $x^{2} - 2pxy - y^{2} = 0$ is
$\frac{x^{2} - y^{2}}{1 - ( - 1)} = \frac{xy}{- p}$
$\Rightarrow \ x^{2} + \frac{2xy}{p} - y^{2} = 0$
Above lines will be same as the $x^{2} - 2qxy - y^{2} = 0.$
$\therefore\ \frac{1}{p} = - q$
$\Rightarrow \ pq = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.