Question

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

• A. $1:2$
• B. $2:1$
• C. $3:4$
• D. $4:3$

Answer 1

The correct option is C $3:4$

$\because$ both the lines are parallel to each other and origin lies in between them
$\therefore$ any line passes through origin and intersecting the given line will be devided by the origin in a fixed ratio and the ratio will be the distance of the origin from the lines
so ratio will be $\frac{9}{\sqrt{20}}:\frac{6}{\sqrt{5}}=3:4$