A line passing through origin and is perpendicular to two given lines `2x+y+6=0` and `4x+2y-9=0`. The ratio in which the origin divides this line is

Options

A. `1:2`
B. `2:1`
C. `4:2`
D. `4:3`

Answer

D

Explanation

Equation of line perpendicular to `2x+y+6=0` and passes through origin is `x-2y=0`
Now point of intersection of `2x+y+6=0` and `x-2y=0` is `(-12/5,-6/5)`. Similarly point of intersection of `x-2y=0` and `4x+2y-9=0` is `(9/5,9/10)`
Let the origin divides the line `x-2y=0` in the ratio `lamda:1`
Then `x=(9/5 lamda-12/5)/(lamda+1)`
`implies0=(9//5 lamda-12//5)/(lamda+1)implies9/5 lamda =12/5`
`:.lamda=12/9=4/3`