# How to find plot all traces of a surface

How can I find all the level curves of the 3-D cylinder $x^2+2z^2=1$?

I want the level curves obtained by fixing (1) $x=k,$ (2) $y=k$ and (3) $z=k$ for some values of $k$ and I would like the graphs of the traces to lie in the corresponding 2D plane and not on the 3D surface.

Is there a feature that allows me to find all 3 traces for some values of $k$ at the same time just by inserting the surface? I would like 3 2-D graphs, one each corresponding to (1), (2), and (3).

For example, the traces should be in planes as in the following: • does this give something close to what you need? k = 0; ContourPlot3D[ x^2 + 2 z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, MeshFunctions -> {# &, #2 &, #3 &}, Mesh -> {{k}, {k}, {k}}] – kglr Apr 23 '17 at 23:22
• I would like to have each of the level curves on a separate plane. For example, the circles obtained by letting $y=k$ should be on a 2-D xz plane, and so on. – The Substitute Apr 23 '17 at 23:28

k = 1/2;
facegrids = {#, {{k}, {k}}} & /@ Join[#, -#] &@IdentityMatrix;

cp3d = ContourPlot3D[x^2 + 2 z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
ContourStyle -> Directive[Orange, Opacity[0.8], Specularity[White, 30]],
MeshFunctions -> {# &, #2 &, #3 &},
Mesh -> {{{k, Directive[Thick, Red]}}, {{k, Directive[Thick, Green]}},
{{k, Directive[Thick, Blue]}}},
FaceGrids -> facegrids] planes = Graphics3D[{Opacity[.5], InfinitePlane/@
NestList[RotateRight/@#&, {{k, -1,-1}, {k,-1, 1}, {k, 1,1}},3]}]

Show[cp3d, planes] • Although the graphic is very nice, can you place those traces on 3 separate planes (the projection of your level curves onto the corresponding coordinate planes)? I have edited to include an image of the type of planes I am looking for. – The Substitute Apr 23 '17 at 23:52
• Can you make each of the planes facing the viewer such as in the picture I attached? – The Substitute Apr 24 '17 at 0:00
• @TheSubstitute, i should have read your edit before my update:) i will see what i can do. – kglr Apr 24 '17 at 0:02