Four Ellipse Constructions

The most common parametrization of ellipses is:
    c(t) = [ a * cos(t), b * sin(t) ]
Here a is constant and with the ratio parameter above b = a/ratio.
1. The circular directrix is the circle of radius 2a around one (here: the left) focal point. Draw, for any point P on the directrix, its radius and the segment to the other focal point F. The symmetry line between P and F is the the tangent to the ellipse at its intersection with the radius of P.
2. Clearly, this ellipse is an image of the circle of radius a under the affine map (x,y) -> (x, b/a*y).
The demo constructs this map to get the ellipse, point and tangent.