combine two ParametricPlot3D plots

Question

I have the following parametric equations

x0[u_, v_, a_, b_, c_] := a* Cos[u]*Sin[v]
y0[u_, v_, a_, b_, c_] := b* Sin[u]*Sin[v]
z0[u_, v_, a_, b_, c_] := c*Cos[v]

x1[u_, v_, a_, b_, c_] := 0
y1[u_, v_, a_, b_, c_] := b* Sin[u]*Sin[v]
z1[u_, v_, a_, b_, c_] := c*Cos[v]

Now I take the plots

g1 = ParametricPlot3D[{x0[u, v, 10, 3, 2], y0[u, v, 10, 3, 2], 
    z0[u, v, 10, 3, 2]}, {u, 0, 2 \[Pi]}, {v, 0, \[Pi]}, 
   Mesh -> None];

g2 = ParametricPlot3D[{x1[u, v, 10, 3, 2], y1[u, v, 10, 3, 2], 
   z1[u, v, 10, 3, 2]}, {u, 0, 2 \[Pi]}, {v, 0, \[Pi]}, Mesh -> None, 
  PlotStyle -> LightBlue]

How can I combine them in order the second plot to be visible (like an Epilog object for g1)?

I want something like the following output

Show[g2, g1]

but the whole ellipsoid should be plot. Thank you.

Answer 1

g1 = ParametricPlot3D[{x0[u, v, 10, 3, 2], y0[u, v, 10, 3, 2], 
   z0[u, v, 10, 3, 2]}, {u, 0, 2 π}, {v, 0, π}, Mesh -> None, 
  PlotStyle -> Opacity[.5]]

g2 = ParametricPlot3D[{x1[u, v, 10, 3, 2], y1[u, v, 10, 3, 2], 
   z1[u, v, 10, 3, 2]}, {u, 0, 2 π}, {v, 0, π}, Mesh -> None, 
  PlotStyle -> LightBlue]

Show[g1, g2]

Answer 2

Just for fun:

Graphics3D[{Opacity[.5], Scale[#, {3, 1, 1}], Opacity[1], 
    Scale[#, {.001, 1, 1}]} &@Sphere[]]

This (self-contained) short form is possible here because ellipsoids are just scaled spheres.

By the way, the Scale with 0.001 in the x direction is also a good way to render disks in 3D.