An ellipsoid is a surface that can be obtained from a sphere by deforming
it by means of directional scalings, or more generally, of an affine
transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as
the zero set of a polynomial of degree two in three variables. Among quadric
surfaces, an ellipsoid is characterized by either of the two following
properties. Every planar cross section is either an ellipse, or is empty, or
is reduced to a single point (this explains the name, meaning "ellipse-like").
It is bounded, which means that it may be enclosed in a sufficiently large
sphere.
An ellipsoid has three pairwise perpendicular axes of symmetry which intersect
at a center of symmetry, called the center of the ellipsoid.