Mathematics · Parabola

JEE Main 2026 — 21 January, Morning Shift — Question 20

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

Option A:
$5 x-y-3=0$
Option B:
$4 x-5 y+6=0$
Option C:
$x-2 y+3=0$
Option D:
$5 x-4 y+3=0$
Correct

Answer: D

Step-by-step solution

$h=\frac{4 t}{5}$

$\mathrm{k}=\frac{2 \mathrm{t}^{2}}{5}=\frac{2}{5} \cdot\left(\frac{5 \mathrm{~h}}{4}\right)^{2}$

$8 \mathrm{k}=5 \mathrm{~h}^{2}$

$\Rightarrow 5 \mathrm{x}^{2}=8 \mathrm{y}$

$\mathrm{T}=\mathrm{S}_{1}$

$5\left(\mathrm{xx}_{1}\right)-4\left(\mathrm{y}+\mathrm{y}_{1}\right)=5 \mathrm{x}_{1}{ }^{2}-8 \mathrm{y}_{1}$

$5(\mathrm{x})-4(\mathrm{y}+2)=5-8.2$

$5 \mathrm{x}-4 \mathrm{y}+3=0$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 21 January, Morning Shift
Subject: Mathematics
Chapter: Parabola
Topic: Chords connected with a Parabola