Focus of an ellipse vs. cone

  • #1
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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.
 

Answers and Replies

  • #2
tiny-tim
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Hi TheFerruccio! :smile:
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. :smile:
 
  • #3
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that makes sense. So, does the axis of the cone have any geometric significance in this case beyond just what was described?
 
  • #4
tiny-tim
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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 … :blushing:
 

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