Find the equation of the straight line which is at a distance 3 from the origin and perpendicular from the origin to the line makes an angle of `30^@` with the positive direction of the x-axis.

Explanation

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

Here, `\alpha=30^\circ` and `p=3`

Therefore, required equation of line is,
`x\cos 30^\circ+y\sin 30^\circ=3`

`\implies x\frac{\sqrt3}{2}+\frac{y}{2}=3`

`\implies \sqrt3x+y=6`