String and Pins: Building an Ellipse

Move the foci and string length. The pencil point stays where d(P,F1) + d(P,F2) is constant.

Tip: drag either focus (orange/blue) or the yellow pencil point directly on the diagram.

Try this first

Drag one focus closer to the center. Predict: does the ellipse get rounder, or more stretched? Then watch the live sum below — it should stay the same.

Focus distance c

String half-length a

Pencil point t

a
b
c
e = c/a
Equation

What to look for ↓

Teaching Notes

Core Idea

An ellipse is the set of all points where d(P,F1)+d(P,F2) is constant.

Try This

Drag one focus closer to center and predict how the ellipse width and height change.

Teacher Prompt

Ask students to locate where the values of a and b are visible in the shape.

Vocabulary

Major axis: longest diameter.
Minor axis: shortest diameter.
Foci: two defining points of ellipse.