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JEE Main202229 Jun 2022Morning ShiftMathematicsStraight LinesActual

The distance between the two points A and A ' which lie on y = 2 such that both the line segments A B and A ' B (where B is the point 2 , 3 ) subtend angle π 4 at the origin, is equal to

Options

  1. A10
  2. B48 5
  3. C52 5
  4. D3

Correct answer

C. 52 5

Step-by-step solution

Let the slope of O B be m 1 = 3 2 and the slope of O A be m 2 = 2 x Now angle between two lines, tan π 4 = 3 2 - 2 x 1 + 6 2 x i.e. 3 2 - 2 x 1 + 6 2 x = 1 ⇒ 3 x - 4 2 x + 6 = 1 3 x - 4 = ± 2 x + 6 ⇒ x 1 = 10 ,   x 2 = - 2 5 ⇒ A A ' = 10 + 2 5 = 52 5

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