- Alla Stolyarevska
Proposition 2. The ellipse (a>b) with foci F1 and F2, and the major semiaxis a is the locus of points for which the sum of distances to the F1 and F2 is equal to 2*a.
Supplementary problem Proposition 3. The distance from an arbitrary point M on the ellipse to each of the foci is a linear function of its abscissa r1=F1M=a+e*x; r2=F2M=a-e*x: .