Transfer from one ellipse to another

Hi I have 2 ellipses with their appropriate parameters- mean and covariance matrix- called Ellipse A and Ellipse B. They are used to cluster two separate data sets. What I'm missing is to find computation function that can input Ellipse A and output Ellipse. This is not trivial since changing the mean affects the covariance and vice verse. Any help will be greatly appreciated!! thank you Keren

[John D'Errico]

HUH? Changing the mean does NOT change the covariance structure! Unless of course you are doing something totally wrong. But we do not know what you did, so how do we know what you did wrong?