Actionscript 3 :: Find A Tight-fitting, Axis-aligned, Bounding Box Of A Rotated Ellipse?

The AS3 getBounds function returns a rectangle that is not fitting tightly to a rotated ellipse. Instead it returns an axis-aligned rectangle based on the bounds of a rectangle whose width/height corresponds to the max/min diameter of the ellipse and follows its rotation.

Stack Overflow Q/A about the math of ellipses and bounding boxes

Based on this I took a stab at coding a solution in AS3. So far I have been able to produce a rectangle that fits perfectly along the x-axis, but as I rotate my ellipse it acts very weird along the y-axis. Rather than alternating between 2*r_min and 2*r_max while rotating, it alternates between 2*r_min and 0. My best guess is that I have done something wrong when solving the differentiated t for gradient -> infinity...

Here is an example from my code:

var r_max:uint = 45;
var r_min:uint = 20;
var rot:Number = ellipse.rotation * (Math.PI / 180);
var t_nil:Number = Math.atan( -r_min * Math.tan(rot) / r_max);

[Code].....