- Prove that a similarity transform carries an ellipse with center at the origin to another ellipse with the same eccentricity.
- Prove the converse of part (a), i.e., two concentric ellipses with the same eccentricity and major axes on the same line are related by a similarity transform.
- Prove the statements corresponding to parts (a) and (b) for hyperbolas.

**Incomplete.**

Just plug in the tx and you will get the same eccentricity in the similar ellipse. For converse, use the generic equation x^2/a^2 + y^2/(a^2(1-e^2)), and put a substitution a2=a1/t to arrive at the same eccentricity.