Conic Sections: Light, Shape, and Reflection

A modular set of explorable explanations designed for classroom projection and independent student play. Every page works as a readable static explanation first, then adds interaction for deeper discovery.

Start with Module 1 → Jump to a module

Debug tip: append ?debug=1 to any page URL to enable verbose logging and quick self-check tools.

How these pages work

Each module is one short loop. You don't need any prior knowledge — just curiosity.

Read the question at the top of the page.
Predict in your head before you touch anything.
Drag a slider or a point on the diagram.
Check the live numbers below the diagram — were you right?

Stuck? Hit Reset Defaults on any page to return to a safe starting view.

Suggested Sequence

Predict

01. Ellipse Reflection

Hero demo: why rays from one focus hit the other.

Build

02. Ellipse Construction

String-and-pins model with live distance sum.

Morph

03. Eccentricity

Slide from circle to elongated ellipse with reflection behavior.

Toggle

04. Parabola Reflection

Parallel rays converge to focus; reverse mode emits parallel rays.

Probe

05. Hyperbola Reflection

Divergent sibling and telescope-inspired dual-mirror path.

Unify

06. Conic Family

Unified focus-directrix eccentricity model and cone slicer narrative.

Bonus Short Demo

Bonus. Elliptical Pool Table

Launch the focus-to-focus pool-table setup from the short and fire rays in all directions.

How To Use This In Class

Teacher Flow

Project Page 1 first. Ask students to predict where the reflected ray will go before you drag.

Then move into Pages 2 and 3 to connect geometry to equation parameters.

Student Workflow

Each page has one core manipulation and one checkable claim.

Students should change one slider at a time and explain what stayed invariant.

Key Vocabulary

Focus / foci: special point(s) used to define the conic.
Directrix: reference line used with focus for conic definitions.
Eccentricity (e): controls conic type and stretch.