Putting this into Wolfram Alpha, I saw that it is a one-sheeted hyperboloid:
$$2x^2 - 4xz + z^2 - 4yz = 4$$
Would someone be able to explain how to prove this mathematically? I thought this surface had to be of the form:
$$x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$$
I have a feeling it has to do with eigenvalues but I can't quite figure it out...
Hint: You can use quadratic forms techniques from linear algebra. See here.