Drawing an ellipse is easy once you know how. Use the pin and string method to create an approximate figure which is ideal for woodworking.
This is the method I used to make an elliptical table top.
Rather than using a piece of string, find a thin piece of wire such as fishing trace wire, piano wire or guitar string or strong thread that won't stretch.
Draw the the length and breadth axis of the ellipse on a piece of cardboard or MDF. Make sure they are at right angle to each other. Tie two nails to a piece of string or wire the length of the longer diameter. Using the topmost point (A) of the short axis, locate two points (B & C) on the horizontal line that is half the length of the long axis. Insert the two nails into these points.
Keeping the string tight with a pencil, trace the outline of the elliptcal shape.
And there you have it. How to draw an ellipse that is perfectly acceptable has never been easier. For more information about the history and properties of an ellipse, click on this link from Wikipedia.
R J Mitchell designed the Spitfire's distinctive elliptical wing to have the thinnest possible cross-section; this thin wing enabled the Spitfire to have a higher top speed than several contemporary fighters, including the Hawker Hurricane.
Mitchell continued to refine the design until his death from cancer in 1937, whereupon his colleague Joseph Smith took over as chief designer, overseeing the development of the Spitfire through its multitude of variants.
"Mankind is not a circle with a single center but an ellipse with two focal points of which facts are one and ideas the other."