Does the Axis of a Cone Cross Through a Focus of an Ellipse?

[TheFerruccio]

An ellipse is a conic section. If you construct an ellipse using a cone, does the axis of the cone cross through one of the foci of the ellipse?

if so, how can this be shown mathematically?

This is just purely out of curiosity.

 

[tiny-tim]

Hi TheFerruccio!

If you construct an ellipse using a cone, does the axis of the cone cross through one of the foci of the ellipse?

Sorry … noooo.

The foci are the points at which the Dandelin spheres touch the plane of the ellipse (or hyperbola) … see the PF library entry " conic " for details.

 

[TheFerruccio]

that makes sense. So, does the axis of the cone have any geometric significance in this case beyond just what was described?

 

[tiny-tim]

that makes sense. So, does the axis of the cone have any geometric significance in this case beyond just what was described?

Not that I know of …