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Saturday, 31 October

JEE Main · Maths · Conic Sections

Condition for Line to be Tangent

JEE Main asked Condition for Line to be Tangent 7 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022 and 2025. It belongs to General Conic Section, in Conic Sections (Maths). The longest wait between two years asking it was 3 years. In 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 6 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.

00.10.20’170’200.07’210.14’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 4 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
  • 202223 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.

  • Area of quadrilateral from ellipse tangents
  • Condition for line tangent to hyperbola

Difficulty

Easy 0Medium 4Hard 3

3 of the 7 questions had a numerical answer.

Every question

All 7 questions

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

  1. 4 Apr 2025, Shift 2 · Q10Let for two distinct values of p the lines y=x+py=x+p touch the ellipse E:x242+y232=1E:\frac{x^2}{4^2}+\frac{y^2}{3^2}=1 at the points A and B. Let the…HardSingle correct
  2. 24 Jun 2022, Shift 1 · Q15Let λx−2y=μ\lambda x-2y=\mu be a tangent to the hyperbola a2x2−y2=b2a^2x^2-y^2=b^2. Then…MediumSingle correct
  3. 24 Jun 2022, Shift 1 · Q28If two tangents drawn from a point (α,β)(\alpha, \beta) lying on the ellipse 25x2+4y2=125x^2+4y^2=1 to the parabola y2=4xy^2=4x are such that the slope…HardNumerical value
  4. 28 Jul 2022, Shift 1 · Q27For the hyperbola H:x2−y2=1H:x^2-y^2=1 and the ellipse E:x2a2+y2b2=1, a>b>0E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b>0, let the (1) eccentricity of E be reciprocal…HardNumerical value
  5. 25 Jul 2022, Shift 1 · Q28Let the equation of two diameters of a circle x2+y2−2x+2fy+1=0x^2+y^2-2x+2fy+1=0 be 2px−y=12px-y=1 and 2x+py=4p2x+py=4p. Then the slope m∈(0,∞)m\in(0,\infty) of the…MediumNumerical value
  6. 22 Jul 2021, Shift 2 · Q68Let a line L:2x+y=k\mathrm{L}:2x+y=k, k>0k>0 be a tangent to the hyperbola x2−y2=3x^2-y^2=3. If L\mathrm{L} is also a tangent to the parabola…MediumSingle correct
  7. 3 Aug 2021, Shift 1 · Q73If the line αx+βy=1\alpha x + \beta y = 1 touches the hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, then the locus of the point…MediumSingle correct

Shifts: 22 Jul 2021, Shift 2, 3 Aug 2021, Shift 1, 24 Jun 2022, Shift 1, 25 Jul 2022, Shift 1, 28 Jul 2022, Shift 1, 4 Apr 2025, 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