I am trying to plot in spherical coordinates the ellipsoid defined as


This is my code:

ParametricPlot3D[{Cos[u] Sin[v], Sin[u] Sin[v], (1/3 Cos[u] Sin[v])^2 + 
    (1/2 Sin[u] Sin[v])^2 + (1/4 Cos[v])^2 == 1}, {u, 0, 2 π}, {v, -π, π}]

What am I doing wrong? No errors are displayed and an empty frame is all I see.

  • $\begingroup$ Doing Solve[(1/3 Cos[u] Sin[v])^2 + (1/2 Sin[u] Sin[v])^2 + (1/4 Cos[v])^2 == 1, {u, v}] will shed some light on the problem. Mathematica can't get solution there. May be needs some assumptions. Try Reduce to see. $\endgroup$
    – Nasser
    Commented Oct 4, 2013 at 23:55
  • $\begingroup$ The third element of the vector you use makes no sense. In this form, it'll evaluate to True or False (as it's an equality test with ==), which doesn't bode well for plotting anything. $\endgroup$
    – kirma
    Commented Oct 5, 2013 at 7:15

1 Answer 1


Typically, the parametrization is a rescaling of spherical coordinates:

With[{a = 3, c = 2},
 ParametricPlot3D[{3 a Cos[u] Sin[v], 2 a Sin[u] Sin[v], 4 c Cos[v]},
   {u, 0, 2 π}, {v, -π, π}]

Mathematica graphics


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