Level curves of exponential

Question

I have the following two-variable function:

f(x,y) = exp(-x^2-(y-1)^2)

And I need to compute/sketch the level curves for exp(-1), exp(-1/4) and 1. I'm not sure how to go about this, I'm not even sure what the range is so this is a bit daunting.

Any guidance will be greatly appreciated,

Cheers :)

Answer 1

For $e^{-1}$ you get $$x^2 + (y-1)^2=1$$ which is a circle.

For $e^{-1/4}$ you get $$x^2 + (y-1)^2=1/4$$ which is another circle.

For $1=e^{0}$ you get $$x^2 + (y-1)^2=0$$ which is a point.