A Parabola occurs when the plane of section is parallel with a line on the side of the cone. When it is not parallel the section is either a circle, an ellipse, or a hyperbola.
In this demonstration, see how an arbitrary conic section compares with the parabola through the same point.
As the plane of section approaches parallel, the distance between the two foci approaches infinity, and the general conic approaches the parabola in shape.
