Maths · Class 11 · Co-ordinate Geometry

Circles for JEE

Everything you need for this topic on one page: the ideas, the formulas, the traps, and free lectures that explain it well.

Last updated: 26 October 2026

Direct answer

Equation of a circle, tangents and normals, chord of contact, family of circles and position of lines and circles.

Key ideas

Circles: what you must understand

General form x² + y² + 2gx + 2fy + c = 0, centre (−g, −f)
Line is tangent if distance from centre = radius
Two circles: compare distance between centres with radii
Radical axis: S₁ − S₂ = 0

Formula sheet

Must-know formulas for Circles

Radius r = √(g² + f² − c)
Tangent at (x₁, y₁): T = 0
Length of tangent = √S₁
Orthogonal circles: 2g₁g₂ + 2f₁f₂ = c₁ + c₂

One-page formula sheet

Printable Circles formula sheet: formulas, key ideas and traps on one page. Save it as a PDF for offline revision.

Avoid

Common mistakes students make

Sign of centre coordinates
Forgetting the condition r² > 0
Wrong formula for common tangents count

For the exam

How this topic is asked in JEE

Appears frequently. Regular source of questions. Learn the T = 0 and S₁ shortcuts.

Prerequisites: Straight Lines.

NCERT map

Where Circles is in NCERT

Chapter names follow the current rationalised NCERT textbooks. Read these sections before solving PYQs.

Class	Book	Chapter	Sections JEE asks from
Class 11	Mathematics	Conic Sections	Circle; Equation of a Circle; Position of a Point with Respect to a Circle; Tangent to a Circle

JEE Advanced level

A JEE Advanced-level example on Circles

Question. A circle passes through the point (2, 3) and touches the line x + y = 1 at the point (1, 0). Find the equation of the circle.

Show solution

The circle touches line x + y = 1 at (1, 0), so the center lies on the normal to this line at (1, 0). The normal has slope 1 (perpendicular to slope -1), giving the line y = x − 1. So center = (h, h − 1).
Radius = distance from center to (1, 0) = √[(h − 1)² + (h − 1)²] = |h − 1|√2
Since (2, 3) lies on the circle: (2 − h)² + (3 − (h − 1))² = 2(h − 1)²
Expanding: (2 − h)² + (4 − h)² = 2(h − 1)² gives 2h² − 12h + 20 = 2h² − 4h + 2, so h = 9/4
Center = (9/4, 5/4) and r² = 2(5/4)² = 25/8

Answer: (x − 9/4)² + (y − 5/4)² = 25/8, or equivalently 2x² + 2y² − 9x − 5y + 7 = 0

This example was solved twice independently and both solutions agree.

Free lectures

Best free lectures for Circles

Full-chapter free lectures picked from YouTube search results by views, from established JEE channels (mostly in Hinglish). Use the subtopic list to jump straight to the part you need (timestamps come from each video's own chapter list). Watch one, then solve PYQs the same day.

CIRCLES in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced — JEE Wallah, 6:25:06
Jump to a subtopic (15)
- 00:00 Introduction
- 12:48 Equations of circle
- 1:29:35 Intercepts made by Circle
- 2:06:37 Point and circle
- 2:15:01 Line and circle
- 2:20:52 Tangents and normals to a circle
- 2:53:52 Director circle
- 2:59:04 Chords of a circle
- 4:07:31 Pair of Tangents
- 4:11:12 Nature of two circles
- 4:56:41 Family of circles
- 5:06:00 Radical axis and properties
- 5:31:10 Radical center and orthogonal circles
- 5:44:06 PYQs
- 6:22:03 Thank You Bachhon!
Circle FULL CHAPTER | Class 11th Maths | Arjuna JEE — Arjuna JEE, 5:03:42
Jump to a subtopic (18)
- 00:00 Introduction
- 13:35 Various Forms of Circle
- 43:02 Diametric Form of Circle
- 01:04:46 Intercepts Made By a Circle
- 01:33:45 Prametric Co-ordinates
- 01:36:18 Power of a Point & Length of Tangent
- 01:44:29 Equation of Tangent to Circle
- 02:18:59 Director Circle
- 02:24:29 Chord of Contact
- 02:39:13 Chord with a Given Mid Point
- 02:50:43 Nature of 2 Circles
- 03:19:06 Family of Circles
- 03:44:34 Radical Axis
- 03:48:24 Properties of Radical Axis
- 03:55:39 Radical Centre
- 03:57:24 Orthogonal Circles
- 04:05:21 PYQs
- 05:02:00 Thank You Bachoo!!

Practise

Where to practise for free

1 JEE Main 2026 PYQs on Circles, with solutions.
Read the chapter in NCERT textbooks (official, free), then solve its NCERT Exemplar (official, free) questions.
Chapter-wise past questions: JEE Main and Advanced PYQs and question bank.
Timed practice tests: NTA Abhyas practice tests (official, free) and our free mock tests.
See it move: interactive simulation.

FAQs

Frequently asked questions

Is Circles important for JEE Main 2027?

Appears frequently. It is part of the official 'Co-ordinate Geometry' unit in the JEE Main 2027 syllabus.

What are the most important formulas in Circles?

Radius r = √(g² + f² − c); Tangent at (x₁, y₁): T = 0; Length of tangent = √S₁.

How should I study Circles for JEE?

Understand the key ideas from NCERT or one full lecture, learn the formula sheet, then solve 25–30 past JEE questions on the topic. Regular source of questions. Learn the T = 0 and S₁ shortcuts.