Ellipse: Definition

Topic:
Ellipse
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
  1. What happens if you slide the value of ? How does it affect the graph? Does it change the sum ?
  2. What happens if you slide the value of ? How does this affect the graph? Does it affect ?
  3. Can you adjust and so that the figure is a circle?
  4. What happens if ?