JEE Main Maths · Conic Sections

Length of Latus Rectum

Length of Latus Rectum (Conic Sections) was asked 5 times in 5 JEE Main shifts, 2024–2026, out of the 42 shifts Lumi analysed. 2 of the 5 had a numerical answer.

Times asked: 5; in 5 shifts
Years: 2024–2026
Usual format: Single correct; Multi-step
Pattern: New since 2024; repeats across shifts

How it is asked

Eccentricity from common latus rectum
Ellipse axes from latus rectum and eccentricity

Difficulty

Easy 1Medium 3Hard 1

Where it sits

Chapter: Conic Sections. Topic: Ellipse Eccentricity, 20 questions over 10 ideas.

All 5 questions

Newest first, each with its options and official answer.

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
7 Apr 2025, Shift 2 · Q12Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10. If its eccentricity is the minimum value of the…MediumSingle correct
9 Apr 2024, Shift 1 · Q12Let $f(x)=x^2+9$ , $g(x)=\frac{x}{x-9}$ and $a=f\circ g(10)$ , $b=g\circ f(3)$ . If $e$ and $l$ denote the eccentricity and the length of the…EasySingle correct
31 Jan 2024, Shift 1 · Q28Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ be $(\pm5,0)$ and $\sqrt{50}$ ,…MediumNumerical value
31 Jan 2024, Shift 2 · Q14Let $P$ be a parabola with vertex $(2,3)$ and directrix $2x+y=6$ . Let an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ , of…HardSingle correct