What will be the equation of line for which p = 3 and a

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What will be the equation of line for which p = 3 and a = 120° ?

1. x – √3y = 6
2. √3x + y = 6
  (3)
3. – x + √3y = 6
4. x - √3y = 5

Correct Option: C

Here,
p = 3 and α = 120°
We know that equation of line is x cosα + y sinα = p
⇒ x cos 120° + y sin 120° = 3
⇒ x cos (180° – 60°) + y sin (180° – 60°) = 3
⇒ – x cos 60° + y sin 60° = 3
∵ cos (180° – θ) = –cosθ
sin (180° – θ) = sinθ

⇒ -	x	+ y	√3	= 3
	2		2

⇒ – x + √3y = 6