JEE Main 2023 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let an ellipse with centre

(1,0)

and latus rectum of length

\frac{1}{2}

have its major axis along x-axis. If its minor axis subtends an angle

60^\circ

at the foci, then the square of the sum of the lengths of its minor and major axes is equal to ______.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Eccentricity from Minor Axis Subtended Angle

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.