Question

A line passing through origin meets two given parallel lines $4x+2y=9$ & $2x+y+6=0$ at $PandQ$, the ratio in which the origin divide the line segment $PQ$ is $m:n$.Find $m+n$

Answer 1

Slope of lines=-2

Equation of line passing through given line but parallel to line is

y - 0 = -2(x- 0)

y = -2x

2x + y = 0

Ratio is $\frac{|-9-0|}{|6-0|}=\frac{9}{6}=\frac{3}{2}m:n=3:2m+n=3+2=5$