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Coordinate Geometry · Mathematics

Ellipse Lab Simulation

Twenty interactive modules on x²/a² + y²/b² = 1, from the two-pin definition to polars and the director circle. Explore, predict, derive and practise JEE problems.

Interactive virtual lab · no download · works on phones and laptops

Chapter
Conic Sections
For
Class 11 · JEE Main · JEE Advanced
Time
~30 min

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How to use it

  1. 1Pick a module from the menu.
  2. 2Drag the orange points or type exact values.
  3. 3Pan and zoom the board.
  4. 4Use Predict, Derive and Practise; Progress tracks your scores.

What to notice

  • PF₁ + PF₂ = 2a; c² = a² − b²; e = c/a.
  • y = mx + c touches the ellipse iff c² = a²m² + b².
  • Perpendicular tangents meet on x² + y² = a² + b².
  • The normal bisects the angle between the focal radii.

For teachers

A ready-made teaching kit comes with this lab

  • Lesson plan

    31 min, 4 steps

  • Ask the class

    4 questions with answers

  • Quick quiz

    6 questions, printable

  • Key formulas

    5 formulas

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About the Ellipse Lab simulation

The Ellipse Lab is an interactive chapter on the ellipse x²/a² + y²/b² = 1 for JEE, in 20 modules. It begins with the two-pin definition PF₁ + PF₂ = 2a, the anatomy (a, b, c and the foci), eccentricity and the standard equation, then the auxiliary circle and eccentric angle, the focus–directrix property, latus rectum and focal distances, tangents, normals, chords of contact, chords with a given midpoint, the director circle, polars and the reflection property.

Each module draws a live diagram you can drag, pan and zoom, with exact values beside every slider and the equations updating as you move. Predict a result before the board reveals it, read the derivation, and practise on randomised JEE-style problems with hints and worked solutions; the lab keeps track of how you are doing in each module.

Also covers: ellipse jee, eccentricity, auxiliary circle, director circle, tangent to ellipse, normal to ellipse, chord of contact ellipse, focal chord ellipse.

Frequently asked questions

What is the condition for y = mx + c to be a tangent to an ellipse?

c² = a²m² + b².

What is the director circle of an ellipse?

The locus of points from which perpendicular tangents can be drawn: x² + y² = a² + b².

What is the length of the latus rectum of an ellipse?

2b²/a. It is also the shortest focal chord; the longest is the major axis, 2a.

What is the reflection property of an ellipse?

A ray from one focus reflects off the ellipse through the other focus, because the normal bisects the angle between the focal radii.

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