Q. The product of the perpendicular distances from the origin on the pair of straight lines $12x^{2} + 25xy + 12y^{2} + 10x + 11y + 2 = 0$ is
A) $\frac{1}{25}$
B) $\frac{2}{25}$
C) $\frac{3}{25}$
D) $\frac{4}{25}$
Explanation
(b)
$Here,\ a = 12,\ b = 12,\ c = 2,\ g = 5,\ f = \frac{11}{2},\ h = \frac{25}{2}$
Now, product of perpendicular distance from the origin
$= \frac{c}{\sqrt{(a + b)^{2} + {4h}^{2}}} = \frac{2}{\sqrt{0 + 4\left( \frac{25}{2} \right)^{2}}} = \frac{2}{25}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.