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Saturday, 31 October

JEE Main · Maths · Conic Sections

Condition for a Line to Touch a Curve

JEE Main asked Condition for a Line to Touch a Curve once in the 108 shifts Lumi analysed, on 25 Jun 2022, Shift 2. It belongs to Tangents and Normals, in Conic Sections (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
asked once so far

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.

00.050.10’170’200’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 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
  • 20221 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

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

  • Slope of line from tangent to parabola

Difficulty

Easy 0Medium 1Hard 0

The question was multiple choice.

Every question

The question

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

  1. 25 Jun 2022, Shift 2 · Q18If the line y=4+kxy = 4 + kx, k>0k > 0, is the tangent to the parabola y=x−x2y = x - x^2 at the point PP and VV is the vertex of the parabola,…MediumSingle correct

Shift: 25 Jun 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