The correlation matrix of the given covariance is computed and the resulting ellipse is plotted. The radi is computed with the singular value decomposition and the cos/sin is calculated for 100 different degrees.
References
C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter: Statistical Data Analysis
Explained. Applied Environmental Statistics with R. John Wiley and Sons, Chichester, 2008.