Chapter 5 · Class 11-12 & JEE Main/Adv
Circles
41 topics in 15 parts
Standard Equation of a Circle Circle with Centre at Origin General Equation of a Circle Centre and Radius from General Form Condition for a Real Circle Circle on a Diameter
Key ideas
Analytical Comparison & Distinction Matrix
| Analytical Method | Standard Representation | Parametric / Invariant Framework |
|---|---|---|
| Algebraic Nature | Explicit equations relating spatial coordinates | Parameterized using scalar parameters (λ, μ) or vectors |
| Symmetry Usage | Relies on coordinate expansion | Exploits vector dot/cross products for rapid simplification |
| Computational Efficiency | Direct for intercept evaluation | Superior for angles, orthogonal projections, and distances |
| Common Mistake | Sign confusion in determinants | Omitting boundary condition checks |
All 41 topics in Circles
Definition
- General Equation of a Circle
- Equation of Circle with Centre (h,k) and Radius r
- Equation of Circle on a Given Diameter
- Equation of Circle Passing Through Given Three Points
- Parametric Form of Circle
- Intercepts Made on the Axes by a Circle
- Equation of Circle with Typical Conditions
- Equation of Circle Passing Through Two Points Subtending Angle θ
Position of a Point with Respect to a Circle
- Condition of Point Inside/Outside/on the Circle
- Maximum and Minimum Distance of a Point from the Circle
Intersection of a Line and a Circle
- Condition of Line Cutting/Touching/Neither touch nor Cutting a Circle
- Length of Intercept Made by Line on Circle
Tangent to a Circle
- Length of the Tangent from a Point to a Circle
- Points of Contact
- Properties Related to Tangent
- Tangent at Point on Circle
- Tangent in Slope Form
- Tangents from a Point Outside the Circle
- Common Tangents
Normal to a Circle at a Given Point
- Point Form
- Co-Normal Points
Chord of Contact
- Definition, Formula & Locus Based Questions
- Length of Chord of Contact
Equation of the Chord Bisected at a Given Point
- Definition, Formula & Locus Based Questions
Director Circle & Its Equation
- Equation of Director Circle
Different Cases of Two Circles
- Conditions for Various Cases
- Number of Tangents Under Different Cases of Two Circles
Angle of Intersections of Two Circles
- Angle Using Cosine Formula
- Orthogonal Intersection of Circles
Pair of Tangents
- Equation of Pair of Tangents
- Angle Between Pair of Tangents
Radical Axis
- Properties & Locus Questions
- Radical Center
Common Chord of Two Circles
- Equation of Common Chord
- Length of the Common Chord
Family of Circles
- Different Cases of Family of Circles
- Circle Passing Through Points of Intersection
Miscellaneous Problems
- Concyclic Points
- Locus Problems
- Inscribed & Circumscribed Figures
- Circle & Other Conics