Mathematics · Parabola

JEE Main 2026 — 22 January, Morning Shift — Question 16

If the chord joining the points $\mathrm{P}_{1}\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)$ and $\mathrm{P}_{2}\left(\mathrm{x}_{2}\right.$ , $y_{2}$ ) on the parabola $y^{2}=12 x$ subtends a right angle at the vertex of the parabola, then $\mathrm{x}_{1} \mathrm{x}_{2}-\mathrm{y}_{1} \mathrm{y}_{2}$ is equal to

Option A:
$288$
Correct
Option B:
$280$
Option C:
$284$
Option D:
$292$

Answer: A

Step-by-step solution

$\left(\mathrm{x}_{1} \mathrm{y}_{1}\right)=\left(3 \mathrm{t}_{1}^{2}, 6 \mathrm{t}_{1}\right) \&\left(\mathrm{x}_{2} \mathrm{y}_{2}\right)=\left(3 \mathrm{t}_{2}^{2}, 6 \mathrm{t}_{2}\right)$

$\mathrm{t}_{1} \mathrm{t}_{2}=-4$

$x_{1} x_{2}=9\left(t_{1} t_{2}\right)^{2}, y_{1} y_{2}=36 t_{1} t_{2}$

$\mathrm{x}_{1} \mathrm{x}_{2}-\mathrm{y}_{1} \mathrm{y}_{2}=9(16)-36(-4)$

$=144+144$ $=288$

Answer key and solution verified before publishing.

Practise Parabola

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 22 January, Morning Shift
Subject: Mathematics
Chapter: Parabola
Topic: Chords connected with a Parabola