Why do we call them conic sections?

This applet is designed to help you get a sense of why we call conic sections, conic sections. A controls the hight, and r the radius of the two cones. X and Y position the plane left right, and up down. You'll want to mostly use the Y slider, as it positions the plane higher and lower on the cones. The angle slider controls the angle the plane makes with the base of the cone. At a zero angle, you have circles, at an angle between zero and the angle of the sides of the cone ellipses, if the angle matches that of the cone you get parabolas, and if the angle is greater than that of the cone the plane intersects BOTH cones and you get a hyperbola! How cool is that?