Inside/outside check

Given a test point $A$, it is very simple to check if it lies inside the ellipse or outside of it. This check is done by computing the sign of expression:

$$\left(\frac{r}{a_e}\right)^2+\left(\frac{z}{(1-f)a_e}\right)^2 - 1$$ (3)

the point is outside if the sign is positive, inside otherwise.