Find the equation of a line for which p = 8, α = 300°

1.	Find the equation of a line for which p = 8, α = 300°
Answer» Given: p = 8, α = 300° 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 300° + y sin 300° = 8 ⇒ x cos (360° – 60°) + y sin (360° – 60°) = 8 We know, cos (360° – θ) = cos θ, sin (360° – θ) = – sin θ ⇒ x cos60° – y sin60° = 8 ⇒ \(\frac{x}{2}-\frac{\sqrt{3}y}{2}\) ⇒ x – √3y = 16 Hence, the equation of line in normal form is x – √3y = 16

Answer»

Given: p = 8, α = 300°

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 300° + y sin 300° = 8

⇒ x cos (360° – 60°) + y sin (360° – 60°) = 8

We know, cos (360° – θ) = cos θ, sin (360° – θ) = – sin θ

⇒ x cos60° – y sin60° = 8

⇒ \(\frac{x}{2}-\frac{\sqrt{3}y}{2}\)

⇒ x – √3y = 16

Hence, the equation of line in normal form is x – √3y = 16

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