Conic Sections

Set the angle alpha to adjust the shape of the cone and beta to adjust the angle of the plane; alpha is the angle between the edge of the cone and the vertical, and beta is the angle between the plane and the vertical. Use the slider to move the plane through the cone. Note the curve formed by the cross section of the plane with the cone for various combinations of alpha and beta. When is a circle formed? When do you get two intersecting lines?