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JEE Main202429 Jan 2024Evening ShiftMathematicsStraight LinesActual

The distance of the point ( 2 , 3 ) from the line 2 x - 3 y + 28 = 0 , measured parallel to the line 3 x - y + 1 = 0 , is equal to

Options

  1. A4 2
  2. B6 3
  3. C3 + 4 2
  4. D4 + 6 3

Correct answer

D. 4 + 6 3

Step-by-step solution

Let, L 1 : 3 x - y + 1 = 0 and L 2 : 2 x - 3 y + 28 = 0 . Slope, m 1 = 3 = tan θ ⇒ θ = 60 ° ⇒ sin θ = 3 2 , cos θ = 1 2 Now, equation of line passing through 2 , 3 and having slope 3 is, x - 2 1 2 = y - 3 3 2 = r ⇒ 2 x - 3 y + 28 = 0 ⇒ 4 + r - 9 - 3 3 2 r + 28 = 0 ⇒ 2 - 3 3 2 r + 23 = 0 ⇒ r = 46 3 3 - 2 × 3 3 + 2 3 3 + 2 ⇒ r = 46 23 × 3 3 + 2 1 = 4 + 6 3

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