Question

If a straight line passing through the origin $O$ meets the lines $4x+2y=9$ and $2x+y+6=0$ at the points $P$ and $Q$ respectively, then the ratio in which $O$ devides the segment $PQ$ is

• A. $3:4$
• B. $4:3$
• C. $2:5$
• D. $5:2$

Answer 1

The correct option is A $3:4$

Given lines are $4x+2y-9=0$ and $2x+y+6=0$
Since the constant term in the equation of lines have opposite signs, origin lies in between two lines.


So,
$\frac{OP}{OQ}=\frac{OM}{ON}\Rightarrow \frac{OP}{OQ}=\frac{\frac{|9|}{\sqrt{16+4}}}{\frac{|6|}{\sqrt{4+1}}}\Rightarrow \frac{OP}{OQ}=\frac{3}{4}$
$\therefore OP:OQ=3:4$