Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with positive direction of xaxis is `150^@` .

Explanation

The equation of line in the normal form is `x\cos \alpha+y\sin \alpha=p`

Here, `\alpha=150^\circ` and `p=4`

Therefore, required equation of line is,
`x\cos 150^\circ+y\sin 150^\circ=4`

`\implies x\frac{-\sqrt3}{2}+\frac{y}{2}=4`

`\implies -\sqrt3 x+y=8`

`\implies \sqrt3 x-y+8=0`