There are a number of different shapes that can be made from taking a

plane from a full

cone. A full cone is the shape of an

infinite diabolo: imagine this diagram in 3-D.

\ /
\ /
X
/ \
/ \

If a slice is taken horizontally, then a circle occurs. Generic formula: x^{2}+y^{2}=r (radius)

\ / __
_\___/_ / \
\ / | |
X \__/
/ \
/ \

If a slice is taken

obliquely through one of the two halves, an

ellipse can be seen. Generic formula: ax

^{2}+by

^{2}=c

\ _/_
\__//
_/\ / _____
X / \
/ \ \_____/
/ \
/ \

If a slice is taken

parallel with one of the sides of the cone, a

parabola occurs, which extends upwards to infinity. (sample formula: y=nx

^{2}+c)

\ / / | ^^ |
\ / / | |
X / \ /
/ X | |
/ / \ \__/
/ \
/ \

If a slice is taken through both cones, a

hyperbola occurs. (can't remember

formula)

\ |/ \ /
\ | \ /
\ /| \_ _/
X | \_/
/ \|
/ | _
/ |\ _/ \_
/ \
/ \
/ \

This is a

rectangular hyperbola with all angles tending to 45 degrees, due to the

vertical line.