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Saturday, 31 October

JEE Main · Maths · Application of Derivatives

Shortest Distance Between Curves

JEE Main asked Shortest Distance Between Curves 3 times in 3 of the 108 shifts Lumi analysed, in 2021, 2022 and 2025. It belongs to Maxima and Minima, in Application of Derivatives (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.04’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20211 of 24
  • 20200 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.

  • Shortest distance between parabola and circle
  • Shortest distance between two curves

Difficulty

Easy 0Medium 2Hard 1

Every question was multiple choice.

Every question

All 3 questions

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

  1. 3 Apr 2025, Shift 2 · Q17The shortest distance between the curves y2=8xy^2 = 8x and x2+y2+12y+35=0x^2 + y^2 + 12y + 35 = 0 is:MediumSingle correct
  2. 26 Jul 2022, Shift 2 · Q5Let P and Q be any points on the curves (x−1)2+(y+1)2=1(x-1)^2+(y+1)^2=1 and y=x2y=x^2, respectively. The distance between P and Q is minimum for some…HardSingle correct
  3. 24 Feb 2021, Shift 2 · Q63If P is a point on the parabola y=x2+4y=x^2+4 which is closest to the straight line y=4x−1y=4x-1, then the co-ordinates of P are :MediumSingle correct

Shifts: 24 Feb 2021, Shift 2, 26 Jul 2022, Shift 2, 3 Apr 2025, Shift 2.

Same topic

Other ideas in Maxima and Minima

Maxima and Minima has 31 ideas JEE Main has asked; 14 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas