Find the equation

Given: p = 4, α = 150°

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 cos 150° + y sin 150° = 4

cos (180° – θ) = – cos θ , sin (180° – θ) = sin θ

⇒ x cos(180° – 30°) + y sin(180° – 30°) = 4

⇒ – x cos 30° + y sin 30° = 4

⇒

⇒ √3x – y + 8 = 0

Hence, the equation of line in normal form is √3 x – y + 8 = 0