Definition of an Ellipse
Use the mouse to change the value of t.
You will see point B moves along the ellipse path but the foci stay the same. Notice that the length of BF1 and BF2 are changing as t changes. However the sum of these two remains the same. What is the value of the sum?
Now use the mouse to change the value of a and b. What is the sum of BF1 and BF2 when a > b, a < b, and a = b? Compare the value of c2 and |a2 - b2|.