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Saturday, 31 October

JEE Main · Maths · Conic Sections

Condition of tangency

JEE Main asked Condition of tangency 11 times in 11 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Circle Tangents, in Conic Sections (Maths). The longest wait between two years asking it was 2 years. In 2020, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
in 11 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.30.60’170.42’200.03’210.07’220’230.14’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 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
  • 20243 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 of 24
  • 20205 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.

  • Tangent point from circle centre and line
  • Count integer parameters for line meeting circle

Difficulty

Easy 0Medium 7Hard 4

5 of the 11 questions had a numerical answer.

Every question

All 11 questions

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

  1. 29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are 2x−3y=52x-3y=5 and 3x−4y=73x-4y=7. The line joining the points (−227,−4)\left(-\frac{22}{7},-4\right) and…MediumNumerical value
  2. 1 Feb 2024, Shift 1 · Q29Let the line L:2x+y=αL:\sqrt{2}x+y=\alpha pass through the point of the intersection P (in the first quadrant) of the circle x2+y2=3x^2+y^2=3 and the…HardNumerical value
  3. 5 Apr 2024, Shift 2 · Q14Let ABCDABCD and AEFGAEFG be squares of side 4 and 2 units, respectively. The point EE is on the line segment ABAB and the point FF is on…MediumSingle correct
  4. 30 Jun 2022, Shift 1 · Q14Consider three circles : C1:x2+y2=r2C_1 : x^2 + y^2 = r^2 C2:(x−1)2+(y−1)2=r2C_2 : (x-1)^2 + (y-1)^2 = r^2 C3:(x−2)2+(y−1)2=r2C_3 : (x-2)^2 + (y-1)^2 = r^2 If a line L :…HardSingle correct
  5. 29 Jul 2022, Shift 1 · Q8Let a line L pass through the point of intersection of the lines bx+10y−8=0bx + 10y - 8 = 0 and 2x−3y=02x - 3y = 0,…HardSingle correct
  6. 31 Aug 2021, Shift 1 · Q86If the variable line 3x+4y=α3x+4y=\alpha lies between the two circles (x−1)2+(y−1)2=1(x-1)^2+(y-1)^2=1 and (x−9)2+(y−1)2=4(x-9)^2+(y-1)^2=4, without intercepting a chord…HardNumerical value
  7. 5 Sep 2020, Shift 1 · Q64If the common tangent to the parabolas, y2=4xy^2=4x and x2=4yx^2=4y also touches the circle, x2+y2=c2x^2+y^2=c^2, then c is equal to :MediumSingle correct
  8. 3 Sep 2020, Shift 1 · Q75The diameter of the circle, whose centre lies on the line x+y=2x+y=2 in the first quadrant and which touches both the lines x=3x=3 and y=2y=2,…MediumNumerical value
  9. 2 Sep 2020, Shift 1 · Q74The number of integral values of k for which the line, 3x+4y=k3x+4y=k intersects the circle, x2+y2−2x−4y+4=0x^{2}+y^{2}-2x-4y+4=0 at two distinct points is…MediumNumerical value
  10. 9 Jan 2020, Shift 1 · Q65A circle touches the yy-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to…MediumSingle correct
  11. 8 Jan 2020, Shift 2 · Q64If a line, y=mx+cy = mx + \mathrm{c} is a tangent to the circle, (x−3)2+y2=1(x - 3)^2 + y^2 = 1 and it is perpendicular to a line L1\mathrm{L}_1, where…MediumSingle correct

Shifts: 8 Jan 2020, Shift 2, 9 Jan 2020, Shift 1, 2 Sep 2020, Shift 1, 3 Sep 2020, Shift 1, 5 Sep 2020, Shift 1, 31 Aug 2021, Shift 1, 30 Jun 2022, Shift 1, 29 Jul 2022, Shift 1, 29 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 5 Apr 2024, Shift 2.

Same topic

Other ideas in Circle Tangents

Circle Tangents has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas