Q11 of 59 Page 178

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.


Given: Length of the perpendicular from the origin (OM) = 4 units


and line makes an angle with positive direction of x – axis


∠BAX = 120°


∴ ∠BAO = 180° - 120° = 60°


∴ ∠MAO = 60°


Now, In Δ AMO,


∠MAO + ∠AOM + ∠OMA = 180°


[∵ sum of angles of a triangle is 180°]


⇒ 60° + θ + 90° = 180°


⇒ 150° + θ = 180°


⇒ θ = 180° - 150°


⇒ θ = 30°


∴ ∠AOM = 30°


Now, we find the equation in NORMAL FORM


xcosθ + ysinθ = p


⇒ xcos(30°) + ysin(30°) = 4


[given: p = 4]



⇒ √3x + y = 8


Hence, the required equation is √3x + y = 8


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