Intersection of a Cone and a Plane: The Conic Sections
The conic sections can be formed by the points of intersection of of a cone and plane. When the slope of the rotating plane is equal to that of the edge of the cone (along the x-z plane), you have a parabola (in this case, when m = 1). When the slope of the plane is greater than that of the cone (m > 1), you have a hyperbola. If -1 < m < 1, you have an ellipse.