I have two ellipses each centered at the origin and defined by:
- Semi major axis $a$
- Semi minor axis $b$
- Angle $\psi$, which is the angle of $a$ counterclockwise from the positive $x$ axis
I add them together such that, if you parametrize an ellipse as $r(\theta)$, then $r_{sum}(\theta)=r_1(\theta)+ r_2(\theta)$.
Is it possible to express the new ellipse as a function of the parameters of the other two, so a function of $(a_1, a_2, b_1, b_2, \psi_1, \psi_2)$?
I hope this makes sense.