Why are They Called Conic Sections Anyways?
I know, you’re still wondering why these are called conic sections. That’s because each is the intersection of a cone and a plane. The cone has to be an infinite double cone, like two cones joined at their tips, one pointing up and one pointing down. A plane can cut through one cone, say the top cone, and create a circle or an ellipse. Now tilt the plane up at a steeper angle, so that it intersects the top cone and runs parallel to the bottom cone. This perfectly balanced conic section is the parabola. Tilt the plane just a bit more, so it intersects both cones, and find the two branches of a hyperbola. That’s the idea; the proof is presented in the next section. The degenerate conic sections also result from a plane and a double cone. Cut across the common apex and find a single point. Let the plane run straight up through both cones, through the common apex, and find two intersecting lines. Finally, a plane can run tangent to the left of the lower cone and the right of the upper cone
