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- How does an ellipse defined by two foci relate to an ellipse defined by one focus?

An ellipse is a conic section - a slice through a cone. The axis of the cone coincides with the focus of the ellipse.(Correct?)

But ellipses can have two foci, not just one, as shown by this method of construction:

Questions:

1. Is F1 in the diagram the same as the axis of the conic section?

2. Does F2 have any correlation in the conic model?

3. Is there some way that these two

But ellipses can have two foci, not just one, as shown by this method of construction:

Questions:

1. Is F1 in the diagram the same as the axis of the conic section?

2. Does F2 have any correlation in the conic model?

3. Is there some way that these two

*apparently*unrelated definitions of an ellipses are two sides of the same coin?