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JEE Main202118 Mar 2021Morning ShiftMathematicsStraight LinesActual

The equation of one of the straight lines which passes through the point ( 1 , 3 ) and makes an angles tan - 1 ( 2 ) with the straight line, y + 1 = 3 2 x is

Options

  1. A4 2 x + 5 y - ( 15 + 4 2 ) = 0
  2. B5 2 x + 4 y - ( 15 + 4 2 ) = 0
  3. C4 2 x + 5 y - 4 2 = 0
  4. D4 2 x - 5 y - ( 5 + 4 2 ) = 0

Correct answer

A. 4 2 x + 5 y - ( 15 + 4 2 ) = 0

Step-by-step solution

y = m x + c 3 = m + c 2 = m - 3 2 1 + 3 2 m ⇒ 6 m + 2 = ± m - 3 2 from Positive sign ⇒ 5 m = - 4 2   ⇒ m = - 4 2 5 from negative sign ⇒ 6 m + 2 = - m + 3 2 ⇒ 7   m = 2 2 ⇒ m = 2 2 7 According to options take m = - 4 2 5 So y = - 4 2 x 5 + 3 + 4 2 5 4 2 x + 5 y - ( 15 + 4 2 ) = 0

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