The Foci Of An Ellipse

Question

In Wikipedia the definition of and ellipse is the following.

An ellipse is a set of points, such that for any point $P$ of the set, the sum of the distances $|PF_{1}|, |PF_{2}|$ to two fixed points $F_{1},F_{2}$, the foci, is constant, usually denoted by $2 a$.

Then the following image is given:

Why is the the sum of the distances $|PF_{1}|$ and $|PF_{2}|$ is $2a$?

Answer 1

$$PF_1+PF_2=V_1F_1+V_1F_2=V_2F_2+V_1F_2=2a$$

Answer 2

This is the definition of an ellipse - the shape that you get when the sum of lengths is constant. Now, if your question is why this sum of lengths is exactly equal to the length major axis, then you can just take note that the maximum extent will be achieved when both lines are in the same direction, which gives Michael Rozenburg's answer.