k = 1/2;
facegrids = {#, {{k}, {k}}} & /@ Join[#, -#] &@IdentityMatrix[3];

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]