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JEE Main 202621 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2026 · 21 January · Morning Shift · Mathematics · Parabola

Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on...

Let O be the vertex of the parabola x2=4yx^{2}=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 2:32: 3 be the conic C. Then the equation of the chord of CC, which is bisected at the point (1,2)(1,2), is :

Options

  1. A5x−4y+3=05 x-4 y+3=0
  2. B5x−y−3=05 x-y-3=0
  3. C4x−5y+6=04 x-5 y+6=0
  4. Dx−2y+3=0x-2 y+3=0

Correct answer

A. 5x−4y+3=05 x-4 y+3=0

Step-by-step solution

Parabola x2=4yx^2 = 4y, vertex O = (0, 0), Q = (2t,t2)(2t, t^2) on parabola.
P divides OQ in ratio 2:3: P=(4t5,2t25)P = \left(\frac{4t}{5}, \frac{2t^2}{5}\right).
Eliminating tt: x2=8y5x^2 = \frac{8y}{5} (conic C with a=25a = \frac{2}{5}).
For chord with midpoint (h,k)(h, k): hx−2ay=h2−2akhx - 2ay = h^2 - 2ak.
At (1,2)(1, 2): x−4y5=1−85=−35x - \frac{4y}{5} = 1 - \frac{8}{5} = -\frac{3}{5}.
5x−4y+3=05x - 4y + 3 = 0.
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