How do I accomplish this rotation?

Here you go: ellipse.zip.......

One small point of query, is the shape in your posted drawing an ellipse?

I had to convert the drawing to be able to open it, and the shape that I saw was a polyline consisting of many small lines. When I tried to draw an ellipse from your axes, the shape did not match yours.

I see the same thing, eldon.

In the drawing that the OP posted the "ellipses" were actually polylines. I imagine that at some point the ellipse he was working with was converted to a polyline. It is worthwhile to note that mathematically, the offset to an ellipse is not an ellipse. This is why when offset is used on an ellipse in AutoCAD a spline is created. It is best to work with a true ellipse entity or a spline as osnap tan can be used. The maximum deviation between a true ellipse and the polyline curve in the drawing is less than 0.2%.

I opened the dwg file and like everyone else its small line segments for that reason the code I posted will work. It will need to be edited for distance bewteen objects and how the object is placed but the method is usable and simple. I tested ellipse's a few problems cropped up. I did think about going to first principles and produce what has been supplied a short segment pline.

Not wanting to be left out, here is a visual method for getting the ellipse focus points (you have to place the points manually using the intersect osnap - doing that in a dynamic block is beyond my brain power).

And a second Dynamic block that I use for disecting angles, I just added a few notes into it to hopefully show how it works. Otherwise just ask

Ellipse and bisect.dwg