Question

A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:

Options

• 1 : 2

• 3 : 4

• 2 : 1

• 4 : 3

Answer 1

3 : 4

Explanation:

Now, distance of origin from 4x + 2y – 9 = 0 is

`|(-9)/sqrt((4)^2 + (2)^2)| = 9/sqrt(20)`

and distance of origin from 2x + y + 6 = 0 is

`|6/sqrt((2)^2 + (1)^2)| = 6/sqrt(5)`

Hence, the required ratio = `(9/sqrt(20))/(6/sqrt(5))`

= `9/sqrt(20) xx sqrt(5)/6`

= `3/4`

= 3 : 4