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Saturday, 31 October

JEE Main · Maths · Conic Sections

Condition for Line Tangency

JEE Main asked Condition for Line Tangency 2 times in 2 of the 108 shifts Lumi analysed, all in 2021. It belongs to General Conic Section, in Conic Sections (Maths). In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
1 of 8
First asked
2021
the only year
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200.07’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20212 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.

  • Common tangent to parabola and ellipse
  • Point not on tangent of given slope to parabola

Difficulty

Easy 0Medium 2Hard 0

Every question was multiple choice.

Every question

All 2 questions

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

  1. 17 Mar 2021, Shift 2 · Q80Let L be a tangent line to the parabola y2=4x−20y^2=4x-20 at (6, 2). If L is also a tangent to the ellipse x22+y2b=1\frac{x^2}{2}+\frac{y^2}{b}=1, then…MediumSingle correct
  2. 25 Feb 2021, Shift 1 · Q71A tangent is drawn to the parabola y2=6xy^2 = 6x which is perpendicular to the line 2x+y=12x + y = 1. Which of the following points does NOT lie…MediumSingle correct

Shifts: 25 Feb 2021, Shift 1, 17 Mar 2021, Shift 2.

Same topic

Other ideas in General Conic Section

General Conic Section has 16 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