IITJEE Advance • Mathematics New Syllabus
Module 12: Circles & Coaxial Systems Hub
Master the advanced geometry of circles. Explore standard forms, tangents and normals, chord properties, radical axes, orthogonal intersections, and coaxial systems.
Topic 1.1 • Circle Basics
Standard, General, and Diametric Forms, Center, Radius, and Axis Intercepts
Topic 1.2 • Relative Positions
Position of a Point, Line-Circle Intersections, and Conditions for Tangency
Topic 2.1 • Curve Geometry
Equations of Tangent and Normal, Point of Contact, and Director Circle
Topic 2.2 • Advanced Chords
Length of Tangent, Pair of Tangents (SS₁ = T²), and Chord with a Given Middle Point
Topic 3.1 • Dual Circles
Relative Position, Touching Circles, and Number/Length of Common Tangents
Topic 3.2 • Angles & Orthogonality
Angle of Intersection Between Circles and Condition for Orthogonal Intersection
Topic 4.1 • Radical Concepts
Equation of Radical Axis (S₁ – S₂ = 0), Properties, and Radical Center
Topic 4.2 • Families of Circles