JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2026, Shift 1, Maths Q10

Question 10 of 75 in this shift, Maths question 10 of 25, Section A.

Let 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 the length of its latus rectum is :

(1) $\frac{4\sqrt5}{3}$
(2) $2\sqrt5$
(3) $\frac{7\sqrt5}{3}$
(4) $\frac{8\sqrt5}{3}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Vertical Ellipse Latus Rectum

Same topic in other shifts

All Ellipse Eccentricity questions

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
3 Apr 2025, Shift 2 · Q12Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with eccentricity $\frac{1}{2}$ and…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.