A cone can be formed by rotating a line:[br]Start with a circle c and a point C that's not in the plane of the circle.[br]Make all lines that go through C and all the points on the circle.[br]In this applet, move point B around the circle, and see the trace of the line BC as B goes around the circle. (To animate B, use the triangular "Play" button at the bottom of the left pane.)[br]Drag the mouse or your finger in the right pane to get different views.[br][br]Move the point C to get a different cone. Then delete the traces from the previous position by clicking the Clear traces button.
In some situations "cone" means a finite cone, with a circle as a base and ending at the vertex.[br]In other situations (such as conic sections) an infinite cone is needed; it continues beyond both the circle and the vertex.[br]To see the finite cone, check Show segment and uncheck Show line.[br][br]Visit Mathematical Intentions at [url=http://www.quadrivium.info]http://www.quadrivium.info[/url] for some history of conic sections.[br][br][b]Troubleshooting:[/b][br]If you get an error message in the 3D window at right, here are some things to try:[br][br][list][*] Try a different browser[/*][*] Research how to enable WebGL in your browser[/*][*] Download the applet file (see the three vertical dots in the upper right of this window) and open it in your own copy of GeoGebra. Download the GeoGebra software at [url=https://www.geogebra.org/download]https://www.geogebra.org/download[/url].[/*][/list]