In the diagram, below, we have two given points, [math]F_1[/math] and [math]F_2[/math]. The distances from these two points to a point [math]P[/math], given by [math]r_1[/math] and [math]r_2[/math] always add up to the same amount.[br][b]Definition of an Ellipse:[/b] The set of all points, the sum of whose distances to two fixed points is a constant.

Questions to Consider[br][list=1][br][*]What happens if you slide the value of [math]b[/math]? How does it affect the graph? Does it change the sum [math]r_1+r_2[/math]?[br][*]What happens if you slide the value of [math]a[/math]? How does this affect the graph? Does it affect [math]r_1+r_2[/math]?[br][*]Can you adjust [math]a[/math] and [math]b[/math] so that the figure is a circle?[br][*]What happens if [math]b>a[/math]?[br][/list]