Critique of cylindrical sections

We have seen that we can define an ellipse as a section of a cylinder. The Classical Greeks didn't develop the theory of ellipses quite this way, although it's pretty certain that they knew it could be done. We're not sure why they chose a method with more difficult proofs; perhaps it was more easily generalizable to other conic sections.

Our findings so far lead to several questions:

• How can we draw an ellipse accurately? Can we do it with straightedge and compass?
  
  
• Are there ways of defining ovals other than ellipses?
  
  
• What properties do ellipses in general share with circles?
  
  
• What happens as we tilt the ellipse's plane more and more?