Eccentricity

One number for all conics

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Eccentricity e unifies the conics: 0 circle, < 1 ellipse, = 1 parabola, > 1 hyperbola.
• Polar orbit: $r = \frac{p}{1 + e\cos\theta}$; farthest/nearest $= \frac{1 + e}{1 - e}$.
• Dandelin spheres touch the cutting plane at the foci.

Steps

1. Focus and directrix, again
2. Design an orbit
3. Earth’s orbit
4. Halley’s comet
5. Pluto’s closest approach
6. Dandelin spheres