are elliptical functions just conic sections?

every second degree polynomial in two variables is a conic

>>8454023
how do you prove this?

>>8454033
You can do it with Spheres too.
http://www.nabla.hr/PC-ConicsProperties2.htm

>>8454016
I finally get the difference between a parabola and hyperbola. With a parabola, the plane is parallel to the edge of the cone. Thank you OP I've been wanting to know this for years now.

>>8454023
I bet every third degree polynomial with three variables is a 3D volume of some 4D cones.

File: IMG_1293.gif (761KB, 499x310px) Image search: [Google]

761KB, 499x310px

>>8454016
Brainlet here.

Are there higher-dimensional generalizations of the concept of conic sections?

>>8454075
>higher-dimensional generalizations
What do you mean?
As in a cone defined in R3? Yeah, there's a ton of ways to define and cut a cone in R3.

>>8454075
>>8455388
He was probably asking if 3D cones, paraboloids, hyperboloids, and ellipsoids are all conic sections of a 4-cone. The answer is yes. If you were to put a 4-plane through it, you'd get those -oids I just mentioned. You could also intersect those again and get the 2D conic sections.