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JEE Main201910 Apr 2019Evening ShiftMathematicsStraight LinesActual

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

Options

  1. A1 4 , - 1 3
  2. B- 1 4 , 2 3
  3. C- 1 4 , - 2 3
  4. D1 4 , 1 3

Correct answer

B. - 1 4 , 2 3

Step-by-step solution

The equation of a line parallel to the line a x + b y + c = 0 is a x + b y + k = 0 . Thus, the equation of a line parallel to 4 x - 3 y + 2 = 0 is 4 x - 3 y + c = 0 . The distance of a line a x + b y + c = 0 from origin is c a 2 + b 2 + c 2 . Given the line 4 x - 3 y + c = 0 is at a distance of 3 5 units from origin ⇒ c 16 + 9 = 3 5 ⇒ c 5 = 3 5 ⇒ c = ± 3 . Hence, the equation of the lines are 4 x - 3 y + 3 = 0 and 4 x - 3 y - 3 = 0 . Clearly point - 1 4 , 2 3 satisfy the given equation 4 x -

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