I want to plot the traces of the level surface of $z=4(x-1)^2+(y+2)^2+3$ parallel to the $xy$-, $zy$-, and $xz$-planes. There is already a similar question and answer but no matter how I change the values, I can not get nice traces of the level curves of $z=4(x-1)^2+(y+2)^2+3$ parallel to the $xy$-, $zy$-, and $xz$-planes. Here is the modified code that I use from the linked question and answer to plot the level curves parallel to the $xy$-plane:
ContourPlot3D[z, {x, -2, 2}, {y, -2, 2}, {z, 0, 4.01},
Contours -> Range[4], ContourStyle -> {Opacity[0.3]},
PlotPoints -> 30, MaxRecursion -> 3, Mesh -> {Range[0.5, 3.5], {0}},
MeshShading -> {
{Opacity[ 0.2], ##} & @@@
("DefaultPlotStyle" /. (Method /. Charting`ResolvePlotTheme["Default", ContourPlot3D])),
{Opacity[0.7], ##} & @@@
("DefaultPlotStyle" /. (Method /. Charting`ResolvePlotTheme["Default", ContourPlot3D]))
},
MeshFunctions -> {#3 &, Function[{x, y, z}, z - (4 (x-1)^2 + (y+2)^2 + 3)]},
MeshStyle -> Directive[Thick, Red], AxesLabel -> {"x", "y", "z"}]
What changes should I make to it so that it would produce nice traces of the level surface of $z=4(x-1)^2+(y+2)^2+3$ parallel to the $xy$-, $zy$-, and $xz$-planes?