I moved this up from an earlier posting as I have had so many questions about how this is done.
Knowing how to draw an accurate ellipse "by eye" can be an extremely useful tool...i.e., from rendering vases and teacups - not to mention its use in portraiture.
Here's how it is done:
Determine the outside dimensions of your ellipse with a rectangle.
Connect the corners of the rectangle with straight lines (CC).
Where these lines intersect is the center, point B.
Divide line BC into thirds by eye and mark with dots.
Point D is the outermost dot and will be moved verrrry slightly outward so that it is a little less than 1/3.
Mark the center of the sides of the rectangle (Point A).
With a dotted curved line, the elipse will only touch the rectangle at Point A and pass through Point D.
Thank heavens this works with any perspective view too and that is when you REALLY need it.
When drawing a circle or any curve, it will always be easier to be accurate if you use a dotted line rather than a solid line first.