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JEE Main202621 January 2026Morning ShiftMathematicsStraight LinesActual

Let a point A lie between the parallel lines L₁ and L₂ such that its distances from L₁ and L₂ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle A B C , where the points B and C lie on the lines L ₁ and L ₂ , respectively, is :

Options

  1. A15 6
  2. B21 3
  3. C12 2
  4. D27

Correct answer

B. 21 3

Step-by-step solution

Let L₂: y = 0 , L₁: y = 9 . Point A at (0, 3) , B at (x_B, 9) , C at (x_C, 0) . AB^2 = x_B^2 + 36 , AC^2 = x_C^2 + 9 , BC^2 = (x_B - x_C)^2 + 81 . From AB = AC : x_B^2 - x_C^2 = -27 . From AB = BC : 2x_Bx_C = x_C^2 + 45 . Solving: 3x_C^4 - 198x_C^2 - 2025 = 0 . Let u = x_C^2 : u^2 - 66u - 675 = 0 u = 75 . a^2 = x_C^2 + 9 = 84 . Area = 3 4 84 = 21 3 .

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