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JEE Main202624 January 2026Evening ShiftMathematicsStraight LinesActual

Let the angles made with the positive x -axis by two straight lines drawn from the point P (2,3) and meeting the line x+y=6 at a distance 2 3 from the point P be ₁ and ₂ . Then the value of ( ₁+ ₂ ) is:

Options

  1. A3
  2. B6
  3. C2
  4. D12

Correct answer

C. 2

Step-by-step solution

Using parametric form through P(2,3) : point at distance r = 2 3 is (2 + r , 3 + r ) . Substituting in x + y = 6 : r( + ) = 1 , so + = 3 2 . 2 ( + 4 ) = 3 2 ( + 4 ) = 3 2 . + 4 = 3 or 2 3 . ₁ = 12 , ₂ = 5 12 . ₁ + ₂ = 12 + 5 12 = 2 .

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