$b^2$ = $a^2$(1-$e^2$), so b = a*sqrt(1-$e^2$). As e -> 0, the ellipse approaches a circle (b -> a). As e -> 1, the ellipse becomes extremely elongated (b -> 0). The latus rectum = 2$b^2$/a = 2a(1-$e^2$). The directrix is at x = $\frac{a}{e}$, always outside the ellipse (since a/e > a for e < 1).