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Question
Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
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Solution
Given that: OM = 4 units
∠BAX = 120°
∴ ∠BAO = 180° – 120° or ∠MAO = 60°
∠MOA + MAO = 90° ......[∵ OM ⊥ AB]
θ + 60° = 90°
∴ θ = 30°
So, equation of AB in its normal form
x cos θ + y sin θ = p
⇒ x cos 30° + y sin 30° = 4
⇒ `x xx sqrt(3)/4 + y xx 1/2` = 4
⇒ `sqrt(3)x + y` = 8
Hence, the required equation is `sqrt(3)x + y` = 8
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