Chapter 21 · Class 11-12 & JEE Main/Adv
Parabola
40 topics in 9 parts
Right-Opening Parabola Left-Opening Parabola Upward-Opening Parabola Downward-Opening Parabola Focus and Directrix Eccentricity of a Parabola
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 40 topics in Parabola
Introduction
- Definition & Focus-Directrix Property
- Condition of 2nd Degree Equation for Conics
- Conic Section as a Locus of a Point
- Important Terms
Standard Equations of Parabola
- Definition & Terminology
- Parabolic Curve & Axis of Symmetry
- Position of a Point with Respect to y² = 4ax
- Shifted Parabolas (y − k)² = 4a(x − h) & (x − h)² = 4a(y − k)
Chord of Parabola
- Equation of a Chord
- Chord Subtending 90° at the Vertex
- Chord Length & Midpoint Loci
- Chord with a Given Midpoint
Intersection of a Line & a Parabola
- Conditions for Intersection & Tangency
- Double Ordinate
- Length of the Intercepted Chord
Equation of Tangent
- Point Form
- Parametric Form
- Slope Form
- Pair of Tangents from an External Point
- Chord of Contact
- Locus of the Intersection of Tangents
- Properties of Tangents
- Perpendicular Tangents & Directrix
Equation of Normal
- Parametric Form
- Slope Form
- Conormal Points & Number of Normals
- Circle Through Conormal Points
- Common Normals
- Properties of Normals
- Reflection Property of a Parabola
Focal Distance & Focal Chord of Parabola
- Focal Distance & Focal Radius
- Focal Chord Properties & Length
- Latus Rectum & Endpoints
Properties of Parabola
- Geometric & Focal Properties
- Inscribed & Circumscribed Figures
- Area & Optimization Problems
- Locus, Reflection & Transformation Problems
Intersection of Parabolas & Conics
- Intersections & Common Tangents of Two Parabolas
- Intersections & Common Tangents of a Parabola & a Circle
- Intersections & Common Tangents of a Parabola & Other Conics