Mathematics · Parabola

JEE Main 2024 — 4 April, Shift 1 — Question 28

Let the length of the focal chord $P Q$ of the parabola $y^{2}=12 x$ be 15 units. If the distance of $P Q$ from the origin is $p$ , then $10 p^{2}$ is equal to $\qquad$

Answer: 72

Numerical answer — enter this value.

Step-by-step solution

length of focal chord $=4 a \operatorname{cosec}^{2} \theta=15$

$12 \operatorname{cosec}^{2} \theta=15$

$\sin ^{2} \theta=\frac{4}{5}$

$\tan ^{2} \theta=4$

$\tan \theta=2$

equation $\frac{y-0}{x-3}=2$

$y=2 x-6$

$2 \mathrm{x}-\mathrm{y}-6=0$

$p=\frac{6}{\sqrt{5}}$

So, $10 \mathrm{p}^{2}=10 \cdot \frac{36}{5}=72$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Parabola
Topic: Chords connected with a Parabola