Similar questions have been asked on Ask Sage before, and solutions or
workarounds were given that work in a general enough case.

Here specifically, the function we study happens to be a quadratic form:

```
f = lambda x, y: 1/4*x^2 + 1/9*y^2
```

In this simple special case, the level set of level `r^2`

, defined by

```
[z == 1/4 * x^2 + 1/9 * y^2, z == r^2]
```

are ellipses, and can be parametrized as

```
x = lambda r: lambda t: 2 * r * cos(t)
y = lambda r: lambda t: 3 * r * sin(t)
z = lambda r: lambda t: r^2
```

and then, defining the x-, y-, z- ranges, min and max as

```
xab = xa, xb = -9, 9
yab = ya, yb = -13, 13
zab = za, zb = 0, 18
```

we can plot the function (with some transparency):

```
p = plot3d(f, xab, yab, zmin=0, zmax=18, opacity=0.5)
```

and superimpose the desired level sets:

```
tau = 2*RDF.pi()
for r in range(5):
p += parametric_plot3d((x(r), y(r), z(r)), (0, tau), color='red')
```

and finally visualize the combination, either with jmol or threejs:

```
p.show(zmin=za, zmax=zb, aspect_ratio=1, viewer='jmol')
p.show(zmin=za, zmax=zb, aspect_ratio=1, viewer='threejs')
```

For other choices of viewers, see the documentation, by doing one of the following:

```
p.show?
help(p.show)
browse_sage_doc(p.show)
```

I could not upload any image since i dont have enough karma for that. Sorry

Welcome to Ask Sage! Thank you for your question!

Please provide your definition of

`f`

. Ideally, one should be able to copy and paste the code you provide in a fresh Sage session, to see what your problem is.I agree that it is not clear what level sets you're seeking to plot. However, the answers to these questions could be helpful https://ask.sagemath.org/question/919...https://ask.sagemath.org/question/896...

Your question has several problems :

Could you refine (rethink ?) your question ?