I have some questions more of curiosity.

I wouldn't seriously mind if no one could answer them:

1. Given a set of points - is there a simple way to construct/compute the ellipsoid with the lowest volume given by

X^{2}/W^{2}+ Y^{2}/H^{2}+ Z^{2}/D^{2}- 1 = 0

that encompasses all points? How about the ellipsoids that have at least one of it's axis-lengths minimized? Does one imply the other?

2. How many distinct points (X,Y,Z) on the surface of such a 3d-ellipsoid are needed to reduce the number of possible solutions to the ellipsoid-equation to one assuming that the points are chosen at random?

I did some googling but didn't find the right things and as I don't think those questions are too easy to answer I decided to simply draw the ellipsoid by eye. Nontheless I would like to hear oppinions. Does someone know a good book dealing with geometric problems of this kind? I tried to construct an ellipsoid through three points by simply substituting in the equation but this didn't get really far.