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The equation of a line which makes an angle of 120o with x-axes and the length of perpendicular from origin on it is 4 units, is
  • a)
    x√3+y+8=0
  • b)
    x√3-y=8
  • c)
    x√3-y=0
  • d)
    x√3+y=0
Correct answer is option 'A'. Can you explain this answer?
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The equation of a line which makes an angle of 120o with x-axes and th...
Equation of the line making an angle of 120o with x-axes
- The equation of a line making an angle of θ with the x-axis is given by: y = mx + c, where m = tanθ.
- In this case, θ = 120o, so m = tan120o = tan(180o - 60o) = -tan60o = -√3.
- Therefore, the equation of the line is y = -√3x + c.

Perpendicular distance from origin to the line
- The perpendicular distance from the origin to a line with equation y = mx + c is given by |c| / √(m^2 + 1).
- Given that the perpendicular distance is 4 units, we have |c| / √(3 + 1) = 4.
- Solving for |c|, we get |c| = 4√4 = 8.

Final equation of the line
- Substituting |c| = 8 back into the equation y = -√3x + c, we get y = -√3x + 8.
- Rearranging the equation, we get x√3 + y + 8 = 0.
- Therefore, the equation of the line is x√3 + y + 8 = 0, which corresponds to option 'A'.
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The equation of a line which makes an angle of 120o with x-axes and the length of perpendicular from origin on it is 4 units, isa)x√3+y+8=0b)x√3-y=8c)x√3-y=0d)x√3+y=0Correct answer is option 'A'. Can you explain this answer?
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