A level curve of f (x, y) is a curve on the domain that satisfies f (x, y) = k It can be viewed as the intersection of the surface z = f (x, y) and the horizontal plane z = k projected onto the domain The following diagrams shows how the level curves f (x, y) = 1 1 − x 2 − y 2 = kA level curve of a function $f(x,y)$ is the curve of points $(x,y)$ where $f(x,y)$ is some constant value A level curve is simply a cross section of the graph of $z=f(x,y)$ taken at a constant value, say $z=c$ A function has many level curves, as one obtains a different level curve for each value of $c$ in the range of $f(x,y)$ We can plot the level curves for a bunch of different constants $c$ together in a level curveGet the free "Level Curves" widget for your website, blog, Wordpress, Blogger, or iGoogle Find more Mathematics widgets in WolframAlpha
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