Let the line y - x =1 intersect the ellipse frac x 2 2 +frac y 2 1 =1 at the points A and B . Then the angle made by the line segment AB at the center of the ellipse is :

Mathematics · Ellipse

JEE Main 2026 — 23 January, Morning Shift — Question 5

Let the line $\mathrm{y}-\mathrm{x}=1$ intersect the ellipse $\frac{\mathrm{x}^{2}}{2}+\frac{\mathrm{y}^{2}}{1}=1$ at the points A and B . Then the angle made by the line segment AB at the center of the ellipse is :

Option A:
$\pi-\tan ^{-1}\left(\frac{1}{4}\right)$
Option B:
$\frac{\pi}{2}+\tan ^{-1}\left(\frac{1}{4}\right)$
Correct
Option C:
$\frac{\pi}{2}+2 \tan ^{-1}\left(\frac{1}{4}\right)$
Option D:
$\frac{\pi}{2}-\tan ^{-1}\left(\frac{1}{4}\right)$

Answer: B

Step-by-step solution

By solving line & equation of ellipse we get $\mathrm{x}=0$ & $\mathrm{x}=-\frac{4}{3}$

$\therefore \mathrm{B}\left(-\frac{4}{3},-\frac{1}{3}\right)$

$\mathrm{m}_{\mathrm{oB}}=\tan \theta=\frac{1}{4}$

$\because \angle \mathrm{AOB}=\frac{\pi}{2}+\theta=\frac{\pi}{2}+\tan ^{-1} \frac{1}{4}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Mathematics
Chapter: Ellipse
Topic: position of a Line or point wrt an Ellipse