B) I'm not very practiced in mapping - so there must be a more elegant way to do your question.
1. Since the rotation has to be done clockwise the angle of rotation is
2. I assume that you know how to rotate the coordinate system by:
where x', y' are the new coordinates after the rotation.
3. With and
Replace the variables x, y in the original equation by x', y' and you have rotated the ellipse around the origin.
4. The new midpoint of the ellipse is
5. Now translate the rotated ellipse by and you'll get:
6. I've attached a sketch.