Question: A line passing through origin and is perpendicular to two given lines $ 2x+y+6=0 $ and $ 4x+2y-9=0 $ , then the ratio in which the origin divides this line is [DCE 2005]
Options:
A)1 : 2
B)2 : 1
C)4 : 3
D)3 : 4
Show Answer
Answer:
Correct Answer: C
Solution:
- Equation of line Perpendicular to $ 2x+y+6=0 $ passes through (0, 0) is $ x-2y=0 $ Now point of intersection of $ x-2y=0 $ and $ 2x+y+6=0 $ is $ ( \frac{-12}{5},\frac{-6}{5} ) $ and point of intersection of $ x-2y=0 $ and $ 4x+2y-9=0 $ is $ ( \frac{9}{5},\frac{9}{10} ) $ .Now say origin divide the line $ x-2y=0 $ in the ratio $ \lambda :1 $ \ $ x=\frac{\frac{9}{5}\lambda -\frac{12}{5}}{\lambda +1}=0\Rightarrow \frac{9}{5}\lambda =\frac{12}{5} $ ,
$ \therefore \lambda =\frac{4}{3} $ Thus origin divides the line $ x=2y $ , in the ratio 4 : 3.
BETA
