$\displaystyle x^2 - y^2 + z^2 = 4 $

We just started this topic, and I am really struggling with it. For this question, you are to use the traces $\displaystyle x=0, y=k, z=0 $ and then identify what this surface is and draw it.

for x=0:

$\displaystyle -y^2 + z^2 = 4 $

$\displaystyle y^2 - z^2 = 4 $ I am not sure, is that a hyperbola?

for y=k:

$\displaystyle x^2+z^2=k^2+4 $ a circle I believe

and z=0:

$\displaystyle x^2-y^2=4$ Hyperbola also..?

If someone could assist me from here on how to identify this graph, I'm a little bit lost.