Mathematics · Parabola

JEE Main 2026 — 8 April, Evening Shift — Question 29

Let O be the vertex of the parabola $y²=4x$ 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 :

Option A:
$1$
Option B:
$2$
Correct
Option C:
$4$
Option D:
$8$

Answer: B

Step-by-step solution

$\mathrm{t}_{1} \mathrm{t}_{2}=-4$ $2 \mathrm{~h}=\mathrm{t}_{1}{ }^{2}+\mathrm{t}_{2}{ }^{2}$ $2 \mathrm{k}=2\left(\mathrm{t}_{1}+\mathrm{t}_{2}\right)$ $2 \mathrm{~h}=\mathrm{k}^{2}-2 \mathrm{t}_{1} \mathrm{t}_{2}$ $2 \mathrm{~h}=\mathrm{k}^{2}+8$ $k^{2}=2 h-8$ $=2((\mathrm{~h}-4)$ L.R. $=2$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 8 April, Evening Shift
Subject: Mathematics
Chapter: Parabola
Topic: Introduction to Parabola