How are the conic sections formed?  Use paper and tape to create a double-napped cone. Then, using scissors, you can but the cone in 4 different ways.

1.  A cut that is parallel to the base of the cone.  The cross section on the surface of the cone is a circle.

2.  A cute that is parallel to one of the sides of the cone. The cut will be through the other side of the cone and the base. This cross-section is a parabola.

3.  A cut through both sides of the cone that is not parallel to the base. The cross-section is an ellipse.

4.  A cut vertical through both cones.  The cross-section is a hyperbola.