Eccentricity and shape of the ellipse

The eccentricity $e = c/a$ is the number that governs the shape of the ellipse, independently of its size. For a fixed semi-major axis $a$, changing $e$ takes us from an almost circular figure to a very elongated one.

Three ellipses with the same semi-major axis $a$ but different eccentricities: the smaller $e$ is, the “rounder” the ellipse; the closer $e$ gets to $1$, the more the ellipse flattens.

In the following simulation you can vary the semi-axes $a$ and $b$ and watch how the foci move and how the eccentricity $e$ changes.

Drag the sliders $a$ and $b$: watch the foci and the eccentricity.

Links

Topics: Ellipse
Concepts: Circle · Eccentricity · Ellipse
Skills: Interpreting a graph · Plotting a graph