Question

The perpendicular form of the origin to a line makes an angle of ${30}^o$ with the y-axis and whose length is 2 units. Find the equation of the line.

Answer 1

According to question,
$p=2$ units
$\theta ={180}^o-{30}^o={150}^o$
then $\sin \theta =\sin {150}^o=-\frac{\sqrt{3}}{2}$
$\cos \theta =\cos {150}^o=-\frac{1}{2}$
Now equation of line
$x\cos \theta -y\sin \theta =p$
$\Rightarrow x\cos {150}^o+y\sin {150}^o=2$
$\Rightarrow x(-\frac{1}{2})-y(-\frac{\sqrt{3}}{2})=2$
$\Rightarrow x-\sqrt{3}y=-4$
$\Rightarrow x-\sqrt{3}y+4=0$