What Are the Level Curves for f(x,y)=e^-(2x^2+2y^2)?

[cue928]

I am being asked to calculate level curves for the following equation:
f(x,y)=e^-(2x^2+2y^2) but I do not know where to start. Any advice on first steps would be greatly appreciated.

 

[SammyS]

Set e^-(2x^2+2y^2) = c, where c is a constant. Solve for x or y.

Once you do that, see if you can come up with a more general solution.

 

[HallsofIvy]

One obvious point: if $e^{-(2x^2+ 2y^2)}= c$ then $-(2x^2+ 2y^2)= ln(c)$ so that $x^2+ y^2= -ln(c)/2$ which is only possible if -ln(c)< 0 which means 0< c< 1. What figures will level curves be?