Ellipsoid is a family of surfaces that can be described by this equation:

(x/a)^2 + (y/b)^2 + (z/c)^2 == 1

It is called ellipsoid because the cross section alone the axes of the surface are ellipses, and the equation's form is the 3D analogue of the equation for ellipses.

Parametric formula:

a = 1; b = 2; c = 2.6;
ParametricPlot3D[{a*Cos[u]*Sin[v], b*Sin[u]*Sin[v], c*Cos[v]}, {u, 0, π}, {v, 0, 2*π}]


Other algebaric surfaces that has cross-sections of conic sections are: ellipsoid, paraboloid, hyperbolic paraboloid, hyperboloid of one sheet, hyperboloid of two sheets.


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