Find the equation of a line for which p = 4, α = 150

1.	Find the equation of a line for which p = 4, α = 150
Answer» 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 ⇒ \(\frac{\sqrt{3}x}{2}+\frac{y}{2}=4\) ⇒ √3x – y + 8 = 0 Hence, the equation of line in normal form is √3 x – y + 8 = 0

Answer»

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

⇒ \(\frac{\sqrt{3}x}{2}+\frac{y}{2}=4\)

⇒ √3x – y + 8 = 0

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

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