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Saturday, 31 October

JEE Main · Maths · Conic Sections

Length of Latus Rectum

JEE Main asked Length of Latus Rectum 12 times in 11 of the 108 shifts Lumi analysed, in 2020, 2022, 2023, 2024, 2025 and 2026. It belongs to Ellipse Eccentricity, in Conic Sections (Maths). The longest wait between two years asking it was 2 years. In 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
12
in 11 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.08’200’210.11’220.07’230.23’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 3 in 24 shifts · 2023: 1 in 12 shifts · 2024: 5 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20245 of 18
  • 20231 of 12
  • 202222 of 24
  • 20210 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

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

Difficulty

Easy 1Medium 8Hard 3

6 of the 12 questions had a numerical answer.

Every question

All 12 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 4 Apr 2026, Shift 1 · Q22Consider the parabola P:y2=4kxP: y^2=4kx and the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1. Let the line segment joining the points of…MediumNumerical value
  2. 7 Apr 2025, Shift 2 · Q12Let the length of a latus rectum of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be 10. If its eccentricity is the minimum value of the…MediumSingle correct
  3. 31 Jan 2024, Shift 2 · Q14Let PP be a parabola with vertex (2,3)(2,3) and directrix 2x+y=62x+y=6. Let an ellipse E:x2a2+y2b2=1, a>bE:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b, of…HardSingle correct
  4. 31 Jan 2024, Shift 1 · Q28Let the foci and length of the latus rectum of an ellipse x2a2+y2b2=1, a>b\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b be (±5,0)(\pm5,0) and 50\sqrt{50},…MediumNumerical value
  5. 1 Feb 2024, Shift 1 · Q13Let x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>ba>b be an ellipse, whose eccentricity is 12\frac{1}{\sqrt{2}} and the length of the latusrectum…MediumSingle correct
  6. 9 Apr 2024, Shift 1 · Q12Let f(x)=x2+9f(x)=x^2+9, g(x)=xx−9g(x)=\frac{x}{x-9} and a=f∘g(10)a=f\circ g(10), b=g∘f(3)b=g\circ f(3). If ee and ll denote the eccentricity and the length of the…EasySingle correct
  7. 5 Apr 2024, Shift 1 · Q15Let the line 2x+3y−k=02x+3y-k=0, k>0k>0, intersect the xx-axis and yy-axis at the points A and B, respectively. If the equation of the circle…MediumSingle correct
  8. 6 Apr 2023, Shift 2 · Q27Let the eccentricity of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 is reciprocal to that of the hyperbola 2x2−2y2=12x^2-2y^2=1. If the…HardNumerical value
  9. 24 Jun 2022, Shift 2 · Q29Let the hyperbola H:x2a2−y2=1H : \frac{x^2}{a^2} - y^2 = 1 and the ellipse E:3x2+4y2=12E : 3x^2 + 4y^2 = 12 be such that the length of latus rectum of HH is…MediumNumerical value
  10. 27 Jul 2022, Shift 1 · Q24An ellipse E:x2a2+y2b2=1E : \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 passes through the vertices of the hyperbola…HardNumerical value
  11. 27 Jul 2022, Shift 1 · Q29If the length of the latus rectum of the ellipse x2+4y2+2x+8y−λ=0x^2 + 4y^2 + 2x + 8y - \lambda = 0 is 4, and ll is the length of its major axis, then…MediumNumerical value
  12. 4 Sep 2020, Shift 1 · Q65Let x2a2+y2b2=1\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a>b)(a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the…MediumSingle correct

Shifts: 4 Sep 2020, Shift 1, 24 Jun 2022, Shift 2, 27 Jul 2022, Shift 1, 6 Apr 2023, Shift 2, 31 Jan 2024, Shift 2, 31 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 5 Apr 2024, Shift 1, 9 Apr 2024, Shift 1, 7 Apr 2025, Shift 2, 4 Apr 2026, Shift 1.

Same topic

Other ideas in Ellipse Eccentricity

Ellipse Eccentricity has 16 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas