Confusion with the eccentricity of ellipse Confusion with the eccentricity of ellipse. On wikipedia I got the following in the directrix section of ellipse.

Each focus F of the ellipse is associated with a line parallel to the minor axis called a directrix. Refer to the illustration on the right, in which the ellipse is centered at the origin. The distance from any point P on the ellipse to the focus F is a constant fraction of that point's perpendicular distance to the directrix, resulting in the equality e = PF/PD. The ratio of these two distances is the eccentricity of the ellipse. This property (which can be proved using the Dandelin spheres) can be taken as another definition of the ellipse.
  Besides the well-known ratio e = f/a, where f is the distance from the center to the focus and a is the distance from the center to the farthest vertices (most sharply curved points of the ellipse), it is also true that e = a/d, where d is the distance from the center to the directrix.

It is given that $e=\frac fa=\frac ad$

In my book it was only given that $e=f/a$ (in my book there is nothing given about directrix of an ellipse).
My question
Knowing that $e=f/a$ how can I get $e=a/d$ and $e=PF/PD$?

Hint: If the eccentricity $e$ & the major axis $2a$ of an ellipse are known then we have the following 


*

*Distance of each focus from the center of ellipse
$$=\text{(semi-major axis)}\times \text{(eccentricity of ellipse)}=\color{red}{ae}$$

*Distance of each directrix from the center of ellipse
$$=\frac{\text{semi-major axis} }{\text{eccentricity of ellipse}}=\color{red}{\frac ae}$$

