JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 August 2021, Shift 1, Maths Q74

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

If the tangents at the points

(2, y)

on the ellipse,

\frac{x^2}{16} + \frac{y^2}{4} = 1

meet the tangent at

(4, y_1)

on it at the points A and B, then the length of the line segment AB is

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

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Intersection of Tangents at Focal Chord Extremities

Same topic in other shifts

All Ellipse Eccentricity questions

2 Apr 2026, Shift 1 · Q10Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a<b$ , pass through the point $(4, 3)$ and have eccentricity $\frac{\sqrt5}{3}$ . Then…MediumSingle correct
4 Apr 2026, Shift 1 · Q22Consider the parabola $P: y^2=4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . Let the line segment joining the points of…MediumNumerical value
5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4, 0)$ and its eccentricity be $\frac{4}{5}$ . If the point…EasySingle correct
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
2 Apr 2025, Shift 1 · Q4If S and S' are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and P be a point on the ellipse, then…MediumSingle correct
2 Apr 2025, Shift 2 · Q12If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the…EasySingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.