Suppose A B is a focal chord of the parabola y 2 =12 x of length l and slope m <√(3) . If the distance of the chord A B from the origin is d , then l d 2 is equal to

Mathematics · Parabola

JEE Main 2024 — 5 April, Shift 1 — Question 30

Suppose $A B$ is a focal chord of the parabola $\mathrm{y}^{2}=12 \mathrm{x}$ of length $l$ and slope $\mathrm{m}<\sqrt{3}$ . If the distance of the chord $A B$ from the origin is $d$ , then $l \mathrm{~d}^{2}$ is equal to $\qquad$

Answer: 108

Numerical answer — enter this value.

Step-by-step solution

$\ell=4 \mathrm{a} \operatorname{cosec}^{2} \theta$

$\ell=12 \times \frac{9}{\mathrm{~d}^{2}}$

$\ell d^{2}=108$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 1
Subject: Mathematics
Chapter: Parabola
Topic: Chords connected with a Parabola