Ellipse segment with points, how do I find the equation and the length of the curve?

[I'm trying]

I have a ellipse that has been rotated. I have the amount of rotation, the beginning point, the highest point, and the ending point of the segment. I need to know how to write an equation for this curved line. I should be able to enter this equation into a graphing calculator and get the exact shape. I also need to know the exact length, can anyone help me?