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Suppose I have used Plot3D command to plot some surface $f(x,y)$. On this plot, I would like to clearly identify some level set of $f(x,y)$, let's say $f(x,y)=0$, and if possible, find the relevant values of $x$ and $y$ for this level set. How could I plot the plane $f(x,y)=0$?

For example I attempt to plot $f(x,y)=x^{2} + y^{2}$ and then indicate the level set $f(x,y)=100$. My code:

Plot3D[{x^2 + y^2, x^2 + y^2 == 100}, {x, -10, 10}, {y, -10, 10},ColorFunction -> "BlueGreenYellow"]

Gives an error. What is wrong?

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You can plot a constant

Plot3D[{x^2 + y^2, 100}, {x, -10, 10}, {y, -10, 10}, ColorFunction -> "BlueGreenYellow"]

enter image description here

or

Plot3D[x^2 + y^2, {x, -10, 10}, {y, -10, 10}, MeshFunctions -> {#3 &}, Mesh -> 1, ColorFunction -> "BlueGreenYellow"]

enter image description here

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  • $\begingroup$ Thanks, both answers are very helpful! $\endgroup$ – Alex Jun 15 '16 at 16:59

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