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

Answer: (D)

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