A degenerate cone results when the intersectoin of a plane with a double napped con is not a parabola, circle, elllipse, or hyperbola.
When a plane parallel to the cone's nappe passes through the cone ,it can creat parabola. What can also be created when a plane passes parallel to the cone's nappe?
How is it created?
When a plane passes parallel to the nappe of a double-napped cone, it can create a hyperbola.
To understand how this is created, let's break it down step by step:
1. Start with a double-napped cone. This is a cone that has two separate "nappes" or cone-shaped sections.
2. Take a plane and position it so that it is parallel to one of the nappes of the cone. This means that the plane does not intersect or touch the cone at any point.
3. Now, visualize how this plane intersects with the cone. Since the plane is not perpendicular to the cone's axis, it will not create a circle or an ellipse. Additionally, since the plane is parallel to the nappe, it will not create a parabola.
4. Instead, when the plane intersects the cone, it creates a curve known as a hyperbola. A hyperbola is a curve that has two separate branches which open up or down. One branch extends from one side of the cone, and the other branch extends from the opposite side.
So, to create a hyperbola when a plane passes parallel to the nappe of a cone, you need to position the plane so that it does not touch or intersect the cone, and it is also parallel to the nappe.