# What's the difference between a parametric equation and a level curve of a function of multiple variables?

For example, the level curve of a function that takes two variables ($$x$$ and $$y$$ for example) and a parametric equation involving two functions ($$x=f(t)=...$$ and $$y=g(t)=...$$). Both of the resulting graphs would be in two dimensional space I believe.

Both of these ideas involving forming a graph determined by a single variable.

I think there is some fundamental difference that I seem to be missing. I've been thinking about this for a long time but maybe my line of thought is in the wrong direction, any help is appreciated.

• When you say "a function that takes two variables," I think of something like this: $f(x,y) = x^2 + y.$ How do you graph such a thing in a two-dimensional space? Instead, such functions are often graphed as a curved surface in three dimensions, using the rule $z=f(x,y).$ Did you mean instead a function of one variable graphed by the rule $y=f(x)$? It may help if you provide some examples that you have encountered. – David K Apr 11 at 14:27
• @DavidK Thank you for the response! Apologies, I was talking about something like $f(x,y)=x^2+y$, which would indeed have to be graphed in three-dimensional space. From what you said and some searching I realized I'm thinking of something called level curves. I think that makes more sense, sorry for the mix up – James Ronald Apr 11 at 14:30
• That is a much better question. – David K Apr 11 at 14:41
• – Christian Blatter Apr 11 at 18:39
• Did that answer (or the other answer to math.stackexchange.com/questions/1251457/…) clear up the issues? – David K Apr 12 at 12:22