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Saturday, 31 October

JEE Main · Maths · Conic Sections

Eccentricity calculation

JEE Main asked Eccentricity calculation 11 times in 11 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to Ellipse Eccentricity, in Conic Sections (Maths). The longest wait between two years asking it was 2 years. In 2020, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
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, 2021, 2022, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.25’200.03’210.11’220.07’230.09’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 3 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20242 of 18
  • 20231 of 12
  • 20223 of 24
  • 20211 of 24
  • 20203 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Relation between conic eccentricities
  • Area of triangle from ellipse focus

Difficulty

Easy 5Medium 3Hard 3

Every question was multiple choice.

Every question

All 11 questions

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

  1. 5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse E:x2a2+y2b2=1E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 be S(4,0)S(4, 0) and its eccentricity be 45\frac{4}{5}. If the point…EasySingle correct
  2. 1 Feb 2024, Shift 2 · Q13Let PP be a point on the ellipse x29+y24=1\frac{x^2}{9}+\frac{y^2}{4}=1. Let the line passing through PP and parallel to yy-axis meet the…HardSingle correct
  3. 1 Feb 2024, Shift 1 · Q12For 0<θ<π/20<\theta<\pi/2, if the eccentricity of the hyperbola x2−y2cosec2θ=5x^2-y^2\mathrm{cosec}^2\theta=5 is 7\sqrt{7} times eccentricity of the…MediumSingle correct
  4. 6 Apr 2023, Shift 2 · Q2In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of…EasySingle correct
  5. 30 Jun 2022, Shift 1 · Q15Let the eccentricity of the ellipse x2+a2y2=25a2x^2 + a^2y^2 = 25a^2 be b times the eccentricity of the hyperbola x2−a2y2=5x^2 - a^2y^2 = 5, where a is the…HardSingle correct
  6. 27 Jun 2022, Shift 1 · Q13Let the eccentricity of an ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>ba>b, be 14\frac{1}{4}. If this ellipse passes through the point…EasySingle correct
  7. 25 Jul 2022, Shift 2 · Q12If the ellipse x2a2+y2b2=1\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 meets the line x7+y26=1\frac{x}{7}+\frac{y}{2\sqrt{6}}=1 on the xx-axis and the line…EasySingle correct
  8. 25 Jul 2021, Shift 1 · Q61Let an ellipse E:x2a2+y2b2=1E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a2>b2a^2>b^2, passes through (32,1)\left(\sqrt{\frac{3}{2}},1\right) and has eccentricity…HardSingle correct
  9. 2 Sep 2020, Shift 2 · Q66For some θ∈(0,π2)\theta\in\left(0,\frac{\pi}{2}\right), if the eccentricity of the hyperbola, x2−y2sec⁡2θ=10x^2-y^2\sec^2\theta=10 is 5\sqrt{5} times the…MediumSingle correct
  10. 9 Jan 2020, Shift 2 · Q65The length of the minor axis (along yy-axis) of an ellipse in the standard form is 43\frac{4}{\sqrt3}. If this ellipse touches the line,…MediumSingle correct
  11. 9 Jan 2020, Shift 1 · Q66If e1\mathrm{e}_1 and e2\mathrm{e}_2 are the eccentricities of the ellipse, x218+y24=1\frac{x^2}{18}+\frac{y^2}{4}=1 and the hyperbola,…EasySingle correct

Shifts: 9 Jan 2020, Shift 2, 9 Jan 2020, Shift 1, 2 Sep 2020, Shift 2, 25 Jul 2021, Shift 1, 27 Jun 2022, Shift 1, 30 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 6 Apr 2023, Shift 2, 1 Feb 2024, Shift 2, 1 Feb 2024, Shift 1, 5 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