On a sheet of paper draw a circle and name its center "F_1". Then pick a point and call it F_2.
Fold the paper so that F_2 meet the circumference at least 50 times (25 points and their opposite through the diameter):
What do you get if the distance between F_1 and F_2 is less than the circle radius?
What do you get if the distance between F_1 and F_2 is greater than the circle radius?
What do you get if the distance between F_1 and F_2 is equal than the circle radius?
By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?

What do you get if the distance between F_1 and F_2 is less than the circle radius?
What do you get if the distance between F_1 and F_2 is greater than the circle radius?
What do you get if the distance between F_1 and F_2 is equal than the circle radius?
By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?