Learn

Saturday, 31 October

JEE Main · Maths · Conic Sections

Family of Circles Touching a Line

JEE Main asked Family of Circles Touching a Line 8 times in 8 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2025 and 2026. It belongs to Circle Tangents, 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
8
in 8 shifts
Years
5 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.07’210.11’220’230’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 3 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20223 of 24
  • 20212 of 24
  • 20201 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.

  • Chord length of circle cut by line
  • Radii of circles touching two lines

Difficulty

Easy 0Medium 4Hard 4

3 of the 8 questions had a numerical answer.

Every question

All 8 questions

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

  1. 6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the xx-axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9, 4) and touching the lines…HardNumerical value
  3. 25 Jun 2022, Shift 1 · Q1Let a circle C touch the lines L1\mathrm{L_1} : 4x−3y+K1=04x-3y+K_1=0 and L2\mathrm{L_2} : 4x−3y+K2=04x-3y+K_2=0, K1,K2∈RK_1, K_2 \in \mathbf{R}. If a line…MediumSingle correct
  4. 24 Jun 2022, Shift 2 · Q27Let a circle C:(x−h)2+(y−k)2=r2C : (x-h)^2 + (y-k)^2 = r^2, k>0k > 0, touch the xx-axis at (1,0)(1, 0). If the line x+y=0x + y = 0 intersects the circle CC at…MediumNumerical value
  5. 25 Jul 2022, Shift 1 · Q29The sum of diameters of the circles that touch (i) the parabola 75x2=64(5y−3)75x^2=64(5y-3) at the point (85,65)\left(\frac{8}{5},\frac{6}{5}\right) and…HardNumerical value
  6. 26 Aug 2021, Shift 2 · Q71A circle C touches the line x=2yx=2y at the point (2, 1)(2,\ 1) and intersects the circle C1:x2+y2+2y−5=0C_1:x^2+y^2+2y-5=0 at two points P and Q such that…HardSingle correct
  7. 4 Aug 2021, Shift 1 · Q73Consider a family of circles which pass through the point (1,1)(1, 1) and touch the axis of yy. If the centre of such a circle is at…MediumSingle correct
  8. 6 Sep 2020, Shift 2 · Q65The centre of the circle passing through the point (0,1)(0,1) and touching the parabola y=x2y=x^2 at the point (2,4)(2,4) is :HardSingle correct

Shifts: 6 Sep 2020, Shift 2, 4 Aug 2021, Shift 1, 26 Aug 2021, Shift 2, 24 Jun 2022, Shift 2, 25 Jun 2022, Shift 1, 25 Jul 2022, Shift 1, 2 Apr 2025, Shift 1, 6 Apr 2026, 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