STRETCH A LINE, and another intersecting it, and rotate the former about the latter and it will sweep out a cone. Now shove this cone through a plane (fig. 1) and mark every point on the plane where the cone touches it. Commonly the result is an ellipse (fig. 2), but if the cone's slope is parallel to the plane it makes a parabola (fig. 3), and if it's parallel to the axis it makes a two-part curve called a hyperbola (fig. 4).