Q. The lines represents by ${ax}^{2} + 2hxy + {by}^{2} = 0$ are perpendicular to each other, if
A) $h^{2} = a + b$
B) $a + b = 0$
C) $h^{2} = ab$
D) $h = 0$
Explanation
(b)
We know, if the line are perpendicular to each other, then $\theta = 90{^\circ}$
$\Rightarrow \ \tan{90{^\circ}} = \frac{2\sqrt{h^{2} - ab}}{a + b}$
$\Rightarrow \ a + b = 0$ [∵ $\tan{90{^\circ}} = \infty\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.