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: x2+y2=r (radius)

```\     /         __
_\___/_        /  \
\ /          |  |
X           \__/
/ \
/   \
```
If a slice is taken obliquely through one of the two halves, an ellipse can be seen. Generic formula: ax2+by2=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=nx2+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.