I confused about how to tell what shape something will be by its formula.

for example..

I know that x^2+y^2=1 is a circle

and

sqrt(x^2+y^2)=1 is a semicircle

but how do you know what a shape like

exp{-x^2-y^2) would be..?

Also are there other types of formulas which include the circle formula, that are common as integration problems?