Question

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

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

Answer 1

Answer: (A)

Since, $P Q \perp O R$

$ \therefore $ Slope of $ P Q \times $ Slope of $ O R=-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 $P Q$ by using
$y-y_1 =m\left(x-x_1\right) $
$y-9 =\frac{2}{9}(x+2) \left(\because x_1=-2, y=9\right)$
$\Rightarrow 9 y-81 =2 x+4$
$\Rightarrow 2 x-9 y+85 =0$