Chapter 11 · Class 11-12 & JEE Main/Adv
Ellipse
47 topics in 9 parts
Standard Ellipse with Horizontal Major Axis Standard Ellipse with Vertical Major Axis Ellipse Focal Relation Eccentricity of an Ellipse Foci of a Horizontal Ellipse Vertices of a Horizontal Ellipse
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 47 topics in Ellipse
Standard Equation & Definitions
- Definition & Basic Terminology of Ellipse
- Standard Equation of Ellipse
- Comparison of Standard Equation of an Ellipse When a>b & a<b
- Equation of an Ellipse Whose Axes are Parallel to Coordinate Axes & Center is (h,k)
- Eccentricity
- Foci & Directrix
- Latus Rectum
- Eccentricity & Latus Rectum
- Focal Distances
- Center & Axes
Auxiliary Circle & Eccentric Angle
- Auxiliary Circle Equation
- Parametric Representation
- Eccentric Angle & Parametric Point
- Properties of Eccentric Angle
- Parametric Equations & Area of Inscribed Triangles
Intersection of Line & Ellipse
- Condition for Tangency
- Length of Intercept
- Condition for Intersection at 2 Points or Touch or Neither Touch nor Cut
Tangent to Ellipse
- Slope Form
- Point Form
- Parametric Form
- Pair of Tangents
- Point of Contact where Line y=mx+c Touches the Ellipse
- Point of Intersection of Tangents at Points P(α) & Q(β)
- Equation of Tangent at Point (a cos θ, b sin θ)
- Equation of Pair of Tangents from Point (h,k)
Normal to Ellipse
- Point Form
- Parametric Form
- Slope Form
- Number of Normals
- Properties of Normals
Director Circle
- Equation of Director Circle
- Properties of Director Circle
Chords of Ellipse
- Chord with Given Midpoint
- Chord of Contact
- Focal Chord
- Equation of Chord Joining Points P(α) & Q(β)
- Length of Chord & Locus of Midpoints
- Equilateral Triangle Inscribed in Ellipse
- Definition, Formula & Locus Based Questions
Focal & Reflection Properties
- Reflection Property
- Focal Distance Property
Intersection & Combination of Conics
- Intersection of Ellipse & Circle
- Intersection of Ellipse & Hyperbola
- Confocal Conics
- Concyclic Points on Ellipse
- General Conic Sections & Intersections