Chapter 12 · Class 11-12 & JEE Main/Adv
Hyperbola
42 topics in 13 parts
Standard Horizontal Hyperbola Standard Vertical Hyperbola Hyperbola Focal Relation Eccentricity of a Hyperbola Foci of a Horizontal Hyperbola Vertices of a Horizontal Hyperbola
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 42 topics in Hyperbola
Hyperbola: Introduction
- Definition & Basic Terminology
- Directrix
- Eccentricity
- Standard Equation of Hyperbola
- General Equation of Hyperbola
- Equation With Axes Parallel to Coordinate Axes & Center (h, k)
- Focal Distance (Focal Radius)
- Latus Rectum
- Transverse & Conjugate Axes
- Position of a Point Relative to a Hyperbola
Conjugate Hyperbola
- Definition & Equation
- Comparison With the Original Hyperbola
Auxiliary Circle & Eccentric Angle
- Auxiliary Circle
- Eccentric Angle & Parametric Point
Asymptotes of Hyperbola
- Definition & Properties
- Angle Between Asymptotes
Rectangular Hyperbola
- Equation Referred to Asymptotes
- Properties
- Concyclic Points
Intersection of a Line & Hyperbola
- Condition for Two Intersections, Tangency or No Intersection
- Double Ordinate
- Length of Chord
Chord of Hyperbola
- Chord Through Two Parametric Points
- Chord With a Given Midpoint
- Focal Chord
- Parametric Equation of a Chord
- Properties of Chords
Equation of Tangent of Hyperbola
- Tangent at Point (x₁, y₁)
- Tangent at a Parametric Point
- Point of Contact for y = mx + c
- Pair of Tangents From a Point
- Intersection of Tangents at Two Parametric Points
Director Circle of Hyperbola
- Definition & Perpendicular Tangents
Equation of Normal of Hyperbola
- Normal at Point (x₁, y₁)
- Normal at a Parametric Point
- Number & Properties of Normals
Chord of Contact
- Equation & Properties
Properties of Hyperbola
- Distance Optimization
Conic Intersections & Combined Conics
- Hyperbola & Circle
- Hyperbola & Ellipse
- Hyperbola & Parabola
- Confocal Conics