Question

The perpendicular from the origin to a line meets it at the point $(-2,9)$. Then, the equation of the line is

• A. $2x-9y+85=0$
• B. $2x+9y-77=0$
• C. $7x+3y-13=0$
• D. $5x+2y-8=0$

Answer 1

Answer: (A)

Since, $PQ\perp OR$

$\therefore$ Slope of $PQ\times$ Slope of $OR=-1$
$\left(\because m_1\times m_2=-1\right)$
$\Rightarrow m\times \frac{y_2-y_1}{x_2-x_1}=-1\Rightarrow m\times \frac{9-0}{-2-0}=-1$
$\Rightarrow \left(\because x_1=0,y_1=0,x_2=-2,y_2=9\right)$
$\Rightarrow m\times \frac{9}{-2}=-1$
$\Rightarrow m=\frac{2}{9}$
Now, equation of $PQ$ by using
$y-y_1=m\left(x-x_1\right)$
$y-9=\frac{2}{9}(x+2)\left(\because x_1=-2,y=9\right)$
$\Rightarrow 9y-81=2x+4$
$\Rightarrow 2x-9y+85=0$