Definition of the Ellipse - Sum of Focal Vectors

The sum of two lines; one from one foci (F1) to a given point on the ellipse curve (x, y), and from the other foci (F2) to the same point (x, y), always equals a constant.

Based on this definition, the following is true: d1 + d2 = constant (2a) as shown in Figure 1 below,

NOTE: To see how the equation of the ellipse can be derived based on this definition - See Appendix A.

   
Figure 1
Equation 1