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Saturday, 31 October

JEE Main · Maths · Conic Sections

Common Tangents to Two Curves

JEE Main asked Common Tangents to Two Curves 4 times in 4 of the 108 shifts Lumi analysed, all in 2022. It belongs to Tangents and Normals, in Conic Sections (Maths). In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
4
in 4 shifts
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210.14’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 4 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20224 of 24
  • 20210 of 24
  • 20200 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.

  • Line tangent to two curves
  • Common tangent to ellipse and hyperbola

Difficulty

Easy 0Medium 3Hard 1

2 of the 4 questions had a numerical answer.

Every question

All 4 questions

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

  1. 26 Jun 2022, Shift 2 · Q11If mm is the slope of a common tangent to the curves x216+y29=1\frac{x^2}{16} + \frac{y^2}{9} = 1 and x2+y2=12x^2 + y^2 = 12, then 12 m212\, m^2 is equal…MediumSingle correct
  2. 29 Jul 2022, Shift 2 · Q27If the tangent to the curve y=x3−x2+xy=x^3-x^2+x at the point (a,b)(a, b) is also tangent to the curve y=5x2+2x−25y=5x^2+2x-25 at the point (2,−1)(2,-1), then…MediumNumerical value
  3. 27 Jul 2022, Shift 2 · Q29A common tangent T to the curves C1:x24+y29=1C_1 : \frac{x^2}{4} + \frac{y^2}{9} = 1 and C2:x242−y2143=1C_2 : \frac{x^2}{42} - \frac{y^2}{143} = 1 does not pass…HardNumerical value
  4. 26 Jul 2022, Shift 2 · Q12The equation of a common tangent to the parabolas y=x2y=x^2 and y=−(x−2)2y=-(x-2)^2 isMediumSingle correct

Shifts: 26 Jun 2022, Shift 2, 26 Jul 2022, Shift 2, 27 Jul 2022, Shift 2, 29 Jul 2022, Shift 2.

Same topic

Other ideas in Tangents and Normals

Tangents and Normals has 20 ideas JEE Main has asked; 7 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas