Q. If the slopes of one of the lines given by ${ax}^{2} + 2hxy + {by}^{2} = 0$ is 5 times the other, then
A) ${5h}^{2} = 9ab$
B) ${5h}^{2} = ab$
C) $h^{2} = ab$
D) ${9h}^{2} = 5ab$
Explanation
(a)
Let the slope of first line be $m,\$then slope of second line is $5m$.
Then, $m + 5m = - \frac{2h}{b}$ and $m \bullet 5m = \frac{a}{b}$
$\Rightarrow \ m = - \frac{2h}{6b} = \frac{- h}{3b}$
$\therefore\ 5m^{2} = \frac{a}{b}\ \Rightarrow \ 5\left( - \frac{h}{3b} \right)^{2} = \frac{a}{b}$
$\Rightarrow \ \frac{{5h}^{2}}{9b^{2}} = \frac{a}{b}\ \Rightarrow \ {5h}^{2} = 9ab$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.