Find the equation of the line on which the 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°.

Question

Philoid · Accepted Answer

Given: p = 4, α = 30∘

Concept Used:

Equation of line in normal form.

Explanation:

So, the equation of the line in normal form is

Formula Used: x cos α + y sin α = p

⇒ x cos30° + y sin30° = 4

⇒ x + y = 4

cos 30°, sin 30°

⇒ √3 x + y = 8

Hence, the equation of line is √3 x + y = 8.