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JEE Main202622 January 2026Morning ShiftMathematicsParabolaActual

If the chord joining the points P ₁ (x₁, y₁ ) and P ₂ (x₂, y₂ ) on the parabola y²=12 x subtends a right angle at the vertex of the parabola, then x₁ x₂-y₁ y₂ is equal to

Options

  1. A284
  2. B280
  3. C288
  4. D292

Correct answer

C. 288

Step-by-step solution

Parabola y^2 = 12x has 4a = 12 , so a = 3 . Parametric points: P₁ = (3t₁^2, 6t₁) , P₂ = (3t₂^2, 6t₂) . Chord subtends right angle at vertex O(0,0) : OP₁ OP₂ = 0 . 9t₁^2 t₂^2 + 36t₁ t₂ = 0 t₁ t₂(t₁ t₂ + 4) = 0 t₁ t₂ = -4 . x₁ x₂ - y₁ y₂ = 9(t₁ t₂)^2 - 36(t₁ t₂) = 9(16) - 36(-4) = 144 + 144 = 288 .

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