How to determine level curves/contours of a 3D function? I have the function $f(x,y) = e^{y/x^2}$ and I need to draw a contour map for levels $e^{-2}$, $e^{-1}$, $1$, $e$, and $e^2$. 
I set $e^{-2}$ equal to the function, and solved for $y$ so that $y = -2x^2$. 
Isn't this curve impossible? What am I doing wrong?
Thanks for your help!

You are lucky in the sense that $f(t)=e^{t}$ is an invertible function. That means that you can just set the argument equal to each other just like you have done. But you would not have been allowed to do so if it wasn't invertible!
For example if you set $(x)^2=(-1)^2$ you can't just assume $x=-1$, because $f(t)=t^2$ is not invertible. You won't catch all solutions then.
