For any point P on the ellipse: SP = a - ex1 and SP' = a + ex1 (where S and S' are foci). Sum: SP + SP' = 2a. Focal chord through focus (ae, 0) has length = 2$b^2$/a * ($\frac{1}{1-e^2*cos^2(alpha}$)) where alpha is the angle with major axis. The minimum focal chord is the latus rectum = 2$b^2$/a.