Place two spheres (red) tangent to the plane (blue) and the cone (light red). The touching points of the plane with the spheres are the small balls within the conic section and form its foci. Consider the two yellow lines connecting a point on the conic section with the top sphere's surface: one line lies within the conic section plane, the other on the surface of the cone. Both are tangent to the top sphere which means they have equal length. The same argument applies to the cyan lines tangent to the bottom sphere. However, the total length of the yellow and the cyan segment on the cone's surface is constant, being the smallest distance (along the cone's surface) between the yellow and cyan circle. Thus, also the total length of the yellow and cyan line segments in the plane of the conic section is constant.