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 = 2b^2/a = 2a(1-e^2). The directrix is at x = a/e, always outside the ellipse (since a/e > a for e < 1).