# Ellipsoid in spherical cordinates

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

$$(x/3a)^2+(y/2a)^2+(z/4c)^2=1$$

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.

• 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. – Nasser Oct 4 '13 at 23:55
• 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. – kirma Oct 5 '13 at 7:15

## 1 Answer

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}]
] 