You find the details of how the third argument of `Ellipsoid` is processed by inspecting the code which is available in the package `MultiDescriptiveStatistics.m`.

 nb = NotebookOpen[ToFileName[{$InstallationDirectory, "AddOns", "Packages", 
 "MultivariateStatistics"}, "MultiDescriptiveStatistics.m"]];
 NotebookFind[nb, "Ellipsoid[mu_?VectorQ, r_?VectorQ, dir_?MatrixQ]"]

![enter image description here][1]


 [1]: https://i.sstatic.net/bGhVy.png