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Calculating coordinates of a point on ellipse border

 
Veronique Kus
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I want to connect lines to different points lying on an ellipse's border.
Does anyone know how I can calculate the coordinates of the point of intersection between the line going from the center to the corner of the bounding rectangle and the ellipse's border? I mean the 4 points which lie to the north-east, north-west, south-east and south-west of the centre of the ellipse (and on its border).

I am also trying to figure out how to find out the coordinates and dimensions of the biggest rectangle completely enclosed by the given ellipse. I guess solving the first problem above would give me an answer to this one...
 
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