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JEE Main20268 April 2026Evening ShiftMathematicsParabolaActual

Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is:

Options

  1. A1
  2. B2
  3. C4
  4. D8

Correct answer

B. 2

Step-by-step solution

Let the vertex of the parabola y^2 = 4x be O(0, 0) . Let the coordinates of the points P and Q on the parabola be (t₁^2, 2t₁) and (t₂^2, 2t₂) respectively. The slope of the chord OP is m₁ = 2t₁ - 0 t₁^2 - 0 = 2 t₁ . The slope of the chord OQ is m₂ = 2t₂ - 0 t₂^2 - 0 = 2 t₂ . Since OP and OQ are perpendicular to each other, m₁ m₂ = -1 . ( 2 t₁ ) ( 2 t₂ ) = -1 t₁ t₂ = -4 Let M(h, k) be the mid-point of the line segment PQ . Then, h = t₁^2 + t₂^2 2 t₁^2 + t₂^2 = 2h k = 2t₁ + 2t₂ 2 t₁ + t₂ = k Squaring the equation for

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