Conic Sections are the intersection of a plane and a cone. The orientation of the plane determines if the intersection is an ellipse, a parabola, the hyperbola, a circle, a point, or a line. The circle, point, and line are generally not considered conics but they are special cases for the location of the plane intersecting the cone.
The sketch at the right is a bit misleading in that the conics do NOT include the areas in color, but rather just the intersectin of the surface of the cone and the plane.
