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JEE Main202621 January 2026Morning ShiftMathematicsParabolaActual

Let O be the vertex of the parabola x²=4 y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2: 3 be the conic C. Then the equation of the chord of C , which is bisected at the point (1,2) , is :

Options

  1. A5 x-4 y+3=0
  2. B5 x-y-3=0
  3. C4 x-5 y+6=0
  4. Dx-2 y+3=0

Correct answer

A. 5 x-4 y+3=0

Step-by-step solution

Parabola x^2 = 4y , vertex O = (0, 0), Q = (2t, t^2) on parabola. P divides OQ in ratio 2:3: P = ( 4t 5 , 2t^2 5 ) . Eliminating t : x^2 = 8y 5 (conic C with a = 2 5 ). For chord with midpoint (h, k) : hx - 2ay = h^2 - 2ak . At (1, 2) : x - 4y 5 = 1 - 8 5 = - 3 5 . 5x - 4y + 3 = 0 .

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