Focus of an ellipse vs. cone

  • #1
TheFerruccio
220
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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
Science Advisor
Homework Helper
25,838
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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
TheFerruccio
220
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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
Science Advisor
Homework Helper
25,838
255
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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