Slicing a Cone

Where the curves come from

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

• Slicing a cone gives a circle, an ellipse, a parabola or a hyperbola.
• The tilt of the plane compared with the cone’s side decides which.
• Ellipses are closed. Parabolas and hyperbolas are open.

Steps

1. Tilt the knife
2. A torch on a wall
3. Dial an eccentricity
4. Through the tip
5. From axes to eccentricity
6. Planetary eccentricity