Question

A line passing through origin and is perpendicular to two given lines $2x+y+6=0$ and $4x+2y-9=0$. The ratio in which the origin divides this line, is

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

Answer 1

The correct option is D $4:3$

Equation of line perpendicular to $2x+y+6=0$ and passes through origin is $x-2y=0$.
Now, the point of intersection of $2x+y+6=0$ and $x-2y=0$ is $(-\frac{12}{5},-\frac{6}{5})$.
Similarly, the point of intersection of $x-2y=0$ and $4x+2y-9=0$ is $(\frac{9}{5},\frac{9}{10})$.
Let the origin divide the line $x-2y=0$ in the ratio $\lambda :1$
Therefore, $x=\frac{\frac{9}{5}\lambda -\frac{12}{5}}{\lambda +1}=0$
$\Rightarrow \lambda =\frac{12}{9}=\frac{4}{3}$