Question

Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.

Answer 1

The normal form of the equation of the line is x cos ω + y sin ω = p.

Here p = 4 and ω = 30°.

Therefore, the equation of the line is x cos 30° + y sin 30° = 4

`x sqrt(3)/2+ y 1/2` = 4

or `sqrt(3) x + y` = 8