A line passing through `(0,0)` and perpendicular to `2x+y+6=0,4x+2y-9=0` then the origin divids the line in the ratio of

Options

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

Answer

D

Explanation

Equation of ine 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 ` lambda:1`
Then ` x = (9/5 lambda-12/5)/(lambda+1) Rightarrow 0 = (9//5 lambda -12//5)/(lamda +1) Rightarrow 9/5 lambda = 12/5`
` lambda = 12/9 = 4/3`