Given two strings, each extending from a different focus to a common point on an ellipse, what is the relationship between the two points? a. they are collinear. b. they have the same slope. c. the sum of their lengths is equal to the length of the major axis. d. the difference of their lengths is equal to the length of the minor axis.

C. The sum of their lengths is equal to the length of the major axis. The definition of an ellipse is the set of all points such that the sum of the distances from those points to the two foci is constant. And option C is pretty much on point for that. In fact, a common method of drawing an ellipse is to place a thumbtack at each foci, then take a length of string and tie into a loop and place that string around the two foci. Finally, using a pencil, draw the ellipse keeping the string tight.