Q. The equation of line parallel to lines $L_{1} \equiv x + 2y - 5 = 0$ and $L_{2} \equiv x + 2y + 9 = 0$ and dividing the distance between $L_{1}\$and $L_{2}$ in the ratio 1 : 6 (internally), is
A) $x + 2y - 3 = 0$
B) $x + 2y + 2 = 0$
C) $x + 2y + 7 = 0$
D) None of these
Explanation
(a)
Let line be $x + 2y + \lambda = 0$
$\therefore\ \lambda = \frac{- 5 \times 6 + 1 \times 9}{7} = - 3\ \ \ \left( \lambda = \frac{mc_{2} + nc_{1}}{m + n} \right)$
So, required line is $x + 2y - 3 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.