Question

If the length of perpendicular from origin to a line is $6$ units and the line makes an angle of ${30}^{\circ }$ with the positive $y-$axis (anti clockwise), then the equation of line is

• A. $\sqrt{3}x-y=12$
• B. $\sqrt{3}x+y=12$
• C. $x+\sqrt{3}y=12$
• D. $x-\sqrt{3}y=12$

Answer 1

The correct option is B $\sqrt{3}x+y=12$

We have
$p=6$
$\alpha ={30}^{\circ }$

So, equation of line is
$x\cos \theta +y\sin \theta =P$
$\Rightarrow x\cos {30}^{\circ }+y\sin {30}^{\circ }=6$
$\Rightarrow \frac{\sqrt{3}}{2}x+\frac{1}{2}y=6$
$\sqrt{3}x+y=12$