Describe the level surfaces of f(x,y,z) = z + sqrt(x^2 + y^2)
The Attempt at a Solution
First of all, what is actually a level surface? Just a normal surface in space?
I followed an example I found on the internet, and this is my attempt at a solution:
First replace f(x,y,z) with a constant
k = z + sqrt(x^2 + y^2)
Then square (k is now another constant)
k = z^2 + x^2 + y^2
This is an ellipsoid, so the level surfaces are ellipsoids centered at the origin.
Is this the right solution? If so, is it possible to say more about the ellipsoids?