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COMEDK20269 May 2026Evening ShiftMathematicsStraight LinesActual

Let the line L₁ be a line passing through the point (0, -6) and making an angle of 150^ with the positive x –axis . Then the equation of a line L₂ parallel to L₁ and crossing the y –axis 2 units below the origin is:

Options

  1. Ax + 3 y + 2 3 = 0
  2. Bx - 3 y + 6 3 = 0
  3. Cx 3 + y + 6 = 0
  4. Dx - 3 y - 2 3 = 0

Correct answer

A. x + 3 y + 2 3 = 0

Step-by-step solution

The slope of line L₁ is m = (150^ ) = - 1 3 . Since line L₂ is parallel to L₁ , the slope of L₂ is also m = - 1 3 . Line L₂ crosses the y -axis 2 units below the origin, so its y -intercept is c = -2 . The equation of line L₂ is given by y = mx + c . Substituting the values of m and c , we get y = - 1 3 x - 2 . Multiplying the entire equation by 3 , we obtain 3 y = -x - 2 3 . Rearranging the terms gives x + 3 y + 2 3 = 0 . Answer: x + 3 y + 2 3 = 0

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