Question

Find equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of ${120}^o$ with the positive direction of $x-$axis.

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

Answer 1

Answer: (C)

$x+\sqrt{3}y=8$

p = 4 units

Equation of the line in normal form is $x\cos 60+y\sin 60=4$

Hence the equation of the line is $x\left(\frac{1}{2}\right)+y\frac{\sqrt{3}}{2}=4$

that is $x+\sqrt{3}y=$8 is the required equation