The angle at which you cut a cone determines the type of curve
A cone shaped like an ice cream cone produces completely different cross-sections depending on the angle at which you cut it with a plane. Adjust the angle with the slider and see a circle, ellipse, parabola, and hyperbola appear in turn.
Four curves: If you cut the cone at a slight angle that is parallel to neither its side nor its base, you get an ellipse. A cut parallel to the base gives a circle. A cut exactly parallel to the side gives a parabola. If you cut more steeply than the side so that the plane passes through the opposite cone as well, you get a hyperbola.
Cutting angle30°
💡 The orbits of planets are ellipses, the paths of cannonballs are parabolas, and the paths of some comets are hyperbolas — these four curves appear throughout nature.