You can define an ellipse using a cone, a set of
points, or by using algebra. For each kind of
definition, explain how to describe a circle as a
special case of an ellipse.

Question

You can define an ellipse using a cone, a set of 
points, or by using algebra. For each kind of 
definition, explain how to describe a circle as a 
special case of an ellipse.

anonymous · Answer

here is a screenshot of the entire question with a picture.

tkhunny · Answer

Well, do it.  For the second, slide $F_{1}\;and\;F_{2}$ closer together, what happens?

scorcher219396 · Answer

For the cone, an ellipse is defined as a horizontal plane through one of the cones. A circle is a horizontal plane through one of the cones that ALSO is perpendicular to the axis of the cone
On an ellipse, the two foci determine how ovalish the ellipse is, a circle also has two foci but they are directly on top of each other, and also in the same place as the center
Algebraically, an ellipse has a major and minor axis, and a circle has a major and minor axis that are ALSO equal to each other