Verified Solution • 2025–26 Session moderate

QJEEM19Maf2e2: JEE Main 2019 Mathematics - Class 11 JEEM19Maf2e2 Solution: Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a…

Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance 35{3 \over 5} from the origin. Then which one of the following points lies on any of these lines ?

Multiple Choice Options

  • A (14,−13)\left( {{1 \over 4}, - {1 \over 3}} \right)
  • B (−14,23)\left( { - {1 \over 4},{2 \over 3}} \right)
  • C (−14,−23)\left( { - {1 \over 4}, - {2 \over 3}} \right)
  • D (14,13)\left( {{1 \over 4},{1 \over 3}} \right)

Step-by-Step Verified Solution

Line parallel to 4x – 3y + 2 = 0

is given as 4x – 3y + λ\lambda = 0

distance from origin is

∣λ5∣=35\left| {{\lambda \over 5}} \right| = {3 \over 5}

⇒λ=±3\Rightarrow \lambda = \pm 3

∴\therefore required lines are 4x – 3y + 3 = 0 & 4x – 3y – 3 = 0

By Putting (−14,23)\left( { - {1 \over 4},{2 \over 3}} \right) on both lines it satisfy.

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