1.nounA surface, all of whose cross sections are elliptic or circular (including the sphere), that generalises the ellipse and in Cartesian coordinates (x, y, z) is a quadric with equation x2/a2 + y2/b2 + z2/c2 = 0.
2.nounSuch a surface used as a model of the shape of the earth.
"Here the geoid is thirty meters below the ellipsoid."