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Saturday, 31 October

JEE Main · Maths · Conic Sections

Common Tangent to Circle and Conic

JEE Main asked Common Tangent to Circle and Conic 9 times in 9 of the 108 shifts Lumi analysed, in 2021, 2022 and 2023. It belongs to Circle Tangents, in Conic Sections (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022 and 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
3 of 8
First asked
2021
last in 2023
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022 and 2023. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210.14’220.14’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 4 in 24 shifts · 2023: 2 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
  • 20232 of 12
  • 20224 of 24
  • 20213 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Circle touching parabola at given point
  • Length between contact points of common tangent

Difficulty

Easy 0Medium 2Hard 7

6 of the 9 questions had a numerical answer.

Every question

All 9 questions

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

  1. 10 Apr 2023, Shift 2 · Q13Let a circle of radius 44 be concentric to the ellipse 15x2+19y2=28515x^2 + 19y^2 = 285. Then the common tangents are inclined to the minor axis of…HardSingle correct
  2. 10 Apr 2023, Shift 1 · Q29Let a common tangent to the curves y2=4xy^2=4x and (x−4)2+y2=16(x-4)^2+y^2=16 touch the curves at the points P and Q. Then (PQ)2(PQ)^2 is equal to…MediumNumerical value
  3. 26 Jun 2022, Shift 1 · Q23Let the common tangents to the curves 4(x2+y2)=94(x^2 + y^2) = 9 and y2=4xy^2 = 4x intersect at the point Q. Let an ellipse, centered at the origin…HardNumerical value
  4. 25 Jun 2022, Shift 1 · Q16If y=m1x+c1y=m_1x+c_1 and y=m2x+c2y=m_2x+c_2, m1≠m2m_1\neq m_2 are two common tangents of circle x2+y2=2x^2+y^2=2 and parabola y2=xy^2=x, then the value of…HardSingle correct
  5. 24 Jun 2022, Shift 1 · Q5Let x2+y2+Ax+By+C=0x^2+y^2+Ax+By+C=0 be a circle passing through (0,6)(0, 6) and touching the parabola y=x2y=x^2 at (2,4)(2, 4). Then A+CA+C is equal to ______.HardSingle correct
  6. 28 Jul 2022, Shift 2 · Q85Two tangent lines l1l_1 and l2l_2 are drawn from the point (2, 0) to the parabola 2y2=−x2y^2=-x. If the lines l1l_1 and l2l_2 are also tangent…HardNumerical value
  7. 26 Feb 2021, Shift 2 · Q90Let L be a common tangent line to the curves 4x2+9y2=364x^2+9y^2=36 and (2x)2+(2y)2=31(2x)^2+(2y)^2=31. Then the square of the slope of the line L is…HardNumerical value
  8. 25 Feb 2021, Shift 2 · Q89A line is a common tangent to the circle (x−3)2+y2=9(x-3)^2 + y^2 = 9 and the parabola y2=4xy^2 = 4x. If the two points of contact (a, b) and (c, d)…HardNumerical value
  9. 31 Aug 2021, Shift 2 · Q89A tangent line L is drawn at the point (2,−4)(2, -4) on the parabola y2=8xy^2 = 8x. If the line L is also tangent to the circle…MediumNumerical value

Shifts: 25 Feb 2021, Shift 2, 26 Feb 2021, Shift 2, 31 Aug 2021, Shift 2, 24 Jun 2022, Shift 1, 25 Jun 2022, Shift 1, 26 Jun 2022, Shift 1, 28 Jul 2022, Shift 2, 10 Apr 2023, Shift 2, 10 Apr 2023, Shift 1.

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