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JEE Main202329 Jan 2023Morning ShiftMathematicsStraight LinesActual

A light ray emits from the origin making an angle 30 ° with the positive x -axis. After getting reflected by the line x + y = 1 , if this ray intersects x-axis at Q, then the abscissa of Q is

Options

  1. A2 ( 3 - 1 )
  2. B2 3 + 3
  3. C2 3 - 3
  4. D3 2 ( 3 + 1 )

Correct answer

B. 2 3 + 3

Step-by-step solution

On plotting the diagram of given data we get, Let Q ( h , 0 ) ∵ O P reflected by x + y = 1 So, the image of Q lies on y = x 3 ∴   x - h 1 = y 1 = - 2 ( h - 1 ) 2 ⇒ x = 1 ,   y = 1 - h Since it lies on y = x 3 ∴   1 - h = 1 3 ⇒ h = 1 - 1 3 = 3 - 1 3 On rationalising the numerator we get, ⇒ h = 3 - 1 3 × 3 + 1 3 + 1 ⇒ h = 2 3 + 3

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