Copy of Ellipse: Definition

In the diagram, below, we have two given points,

and

. The distances from these two points to a point

, given by

and

always add up to the same amount. Definition of an Ellipse: The set of all points, the sum of whose distances to two fixed points is a constant.

Questions to Consider

What happens if you slide the value of ? How does it affect the graph? Does it change the sum ?
What happens if you slide the value of ? How does this affect the graph? Does it affect ?
Can you adjust and so that the figure is a circle?
What happens if ?

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