Question

Equation of straight line on which length of perpendicular from the origin is four units and the line makes an angle ${120}^{\circ }$ with $x-\text{axis}$ is

• A. $x-\sqrt{3}x+8=0$
• B. $\sqrt{3}x-y=-8$
• C. $\sqrt{3}x-y=8$
• D. $\sqrt{3}x+y+8=0$

Answer 1

The correct option is D $\sqrt{3}x+y+8=0$

Given: length of perpendicular from the origin is four units and the line makes an angle ${120}^{\circ }$ with $x-\text{axis}$
$m=\tan \theta =\tan {120}^{\circ }=-\sqrt{3}$
Therefore, Equation of line is
$y=-\sqrt{3}x+c$

$\left|\frac{0+\sqrt{3}.0+c}{\sqrt{1+(\sqrt{3}{)}^2}}\right|=4$
$\left|\frac{c}{2}\right|=4$
$c=\pm 8$
$y+\sqrt{3x}=\pm 8$