I need a little help understanding how to draw ellipses in perspective

[fauxfresh]

Hmm..
EDIT: Forgot to mention, the minor axises (axi? axes?) for each ellipse should go though the center of both ellipses!  The 2nd image didn't illustrate that, ergo, not a cylinder! (Or at least not a cylinder with a circular face)
EDIT 2: As far as I know, in a two point perspective, any four sided shape with at least two lines parallel to each other can be considered as a perfect square. Of course, you can go to the extreme of making one parallel line a 100 feet and 10 cm with the other. I can still say it can be considered a perfect square in perspective, but a horribly distorted perfect square in perspective.

Thank you so much for the explanation! 

I think I understand the concepts now. This is the video where the second image comes from and created so much confusion for me. https://www.youtube.com/watch?v=2GpQMxcHOEU


At 7:09 she connects the two ellipses into a cylinder but now I know that is just a mistake on her part because it is one point perspective and she should have placed another vanishing point.