Eggs Cooked Three Ways

Here are four ellipsoids. Sometimes an egg, sometimes an M&M, but always the same shape name.

The first two - though different color schemes - both show a polar coordinate parametrization. 

Here are the level sets of constant height.  The level sets all are ellipses - hence the name of the shape!

Here are the level sets of constant x-value.  The level sets are all ellipses in this direction as well!