Procedure to find a level curves I'm having trouble finding level curves. What's the procedure? In this case, for example:
$z=x^2+y^2=k$ $\hookrightarrow y=\sqrt(k-x^2)$
Then I sketch this based on knowing the formulas of circunference, parabola, ellipse, etc? Or do I sketch this based on first, second derivatives and general procedures of graph sketching?
Or every formula will lead to common things like hyperbole, parabola, circunferences,etc?
What should I focus my study on? Right now I'm not good in solving level curves problems...
Like finding level curves for this: $$ z=e^{x^2-y^2}$$
Thanks in advance.

Either you use a computer, or you sketch the curves based on recognizing the equation as something you already know.
In the first case you should recognize $x^2+y^2=k$ as the equation for a circle with radius $\sqrt k$ rather than try to rewrite it to get $y$ as a function of $x$.
Similarly for $e^{x^2-y^2}=k$ you would first take the logarithm on both sides to get $x^2-y^2=\log k$ and then recognize the latter as a hyperbola with asymptotes $x=\pm y$ -- or, when $\log k=0$, the crossing lines $x=\pm y$ themselves.
Of course you're not always going to get something you recognizing. In that case it is either the computer, or a lot of labor with pencil and paper to find enough points to connect them freehand.
