If follows immediately that for a point P' outside the ellipse

P'F + P'F' > 2a. Take F (a,b), F' (c, d).

Reflect F' in the x-axis to G (c, -d). Let FG cut the x-axis at P' and let the x-axis touch the ellipse at P. Then since P' is not inside the ellipse FG = FP' + F'P' >= FP + F'P.

But FG <= FP + FP'. Hence equal. So the length of the major axis is