You can 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]"] 