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?