Question

The perpendicular from the origin to a line L meets it at point $(3,-9)$, equation of the line L is

• A. $x-3y=30$
• B. $3x-y=18$
• C. $x+3y+24=0$
• D. $3x+y=18$

Answer 1

The correct option is A $x-3y=30$

REF.Image.

slope of $L_1=\frac{-9}{3}=-3$

Hence, slope of $L_2=\frac{-1}{-3}=\frac{1}{3}$

$\therefore$ Equation of the line 'L' is given by

$y-(-9)=\frac{1}{3}(x-3)$

$\Rightarrow y+9=\frac{1}{3}(x-3)$

$\Rightarrow 3y+27=x-3$

$\Rightarrow x-3y=30$