Consider an ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ as shown where $S$ is the focus , $O$is the center $FE$ is directix such that $PA$ produced meets at $E$ on the directrix and $A'P$ meets on the directrix at $F$. $P$ is any point on the ellipse. $PP'$ is the focal chord. 
Find $\angle FSE$. Also find a constant ratio exists between $\angle ASE$ and $\angle ESP'$ and another ratio between $\angle ASF$ and $\angle FSP$.
One of the ways would be to use force and assign the points according to the ellipse equation. By calculation (which I don't include here due to its length) I got $\angle FSE$ as $90°$.But even those equations are not very helpful to find the angle ratio needed. Is there any near geometrical method to solve the problem?