JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 August 2021, Shift 2, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

If an ellipse passes through the point

(4, 1)

and has foci at

(\pm3, 0)

, then its eccentricity is

(1) $\frac{2\sqrt{2}}{3}$
(2) $\frac{\sqrt{2}}{3}$
(3) $\frac{1}{\sqrt{2}}$ Official answer
(4) $\frac{1}{2}$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Focal distance property

Same idea in other shifts

Asked 3× in all

8 Apr 2026, Shift 2 · Q2The number of values of $z \in \mathbb{C}$ , satisfying the equations $|z - (4 + 8i)| = \sqrt{10}$ and…HardSingle correct
4 Apr 2025, Shift 2 · Q11The centre of a circle C is at the centre of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ . Let C pass through the foci $F_1$ …HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.