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JEE Main2016MathematicsStraight LinesActual

The point 2 , 1 is translated parallel to the line L : x - y = 4 by 2 3 units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is

Options

  1. Ax + y = 2 - 6
  2. B2 x + 2 y = 1 - 6
  3. Cx + y = 3 - 3 6
  4. Dx + y = 3 - 2 6

Correct answer

D. x + y = 3 - 2 6

Step-by-step solution

Equation of line Q R perpendicular to L : x - y = 4 is x + y - c = 0       … 1 Distance of Q R from 2 , 1 is 2 3 ⇒   2 3 = 2 + 1 - c 2 ⇒   2 6 = 3 - c ⇒   c - 3 = ± 2 6   ⇒ c = 3 ± 2 6 Line can be x + y = 3 ± 2 6 x + y = 3 - 2 6 (since Q is in the third quadrant)

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