Mathematics · Parabola

JEE Main 2026 — 6 April, Morning Shift — Question 32

Let chord $PQ$ of length $3\sqrt13$ of the parabola $y²=12x$ be such that the ordinates of points $P$ and $Q$ are in the ratio $1:2.$ If the chord $PQ$ subtends an angle $α$ at the focus of the parabola, then $sin α$ is equal to :

Option A:
$\frac{3}{5}$
Correct
Option B:
$\frac{4}{5}$
Option C:
$\frac{5}{13}$
Option D:
$\frac{12}{13}$

Answer: A

Step-by-step solution

$\mathrm{P}\left(3 \mathrm{t}^{2}, 6 \mathrm{t}\right), \mathrm{Q}\left(12 \mathrm{t}^{2}, 12 \mathrm{t}\right)$ $P Q=\sqrt{81 \mathrm{t}^{4}+36 \mathrm{t}^{2}}$ $81 \mathrm{t}^{4}+36 \mathrm{t}^{2}=117$ $\Rightarrow 9 \mathrm{t}^{4}+4 \mathrm{t}^{2}-13=0$ $\left(\mathrm{t}^{2}-1\right)\left(9 \mathrm{t}^{2}+13\right)=0 \Rightarrow \mathrm{t}=1$ $\mathrm{P}(3,6), \mathrm{Q}(12,12)$ slope of $\mathrm{QS}=\frac{4}{3}$ $\tan \alpha=\frac{3}{4}, \sin \alpha=\frac{3}{5}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 6 April, Morning Shift
Subject: Mathematics
Chapter: Parabola
Topic: Introduction to Parabola