OOps, forgot to add how to find equation for an ellipse. Trace said ellipse onto a piece of cardboard. Take 2 pins and a piece of string. Find the center of the two pins by trial and error by using string. String length will determine the trace shape by using a stick in the middle of the string as it travels the edge of the ellipse as said string is attached to the two pins.

Ellipse equation is 1= x^2/a^2 + y^2/b^2 Where a is the distance between the two ends divided by two of the ellipse, and b is the max distance from the top of the ellipsoid to the pin line.