Level Curves and Cross Sections
Main Concept

A level curve of the surface $zequals;f\left(xcomma;y\right)$ is a twodimensional curve with the equation $f\left(x\,y\right)equals;k$, where k is a constant in the range of f. A level curve can be described as the intersection of the horizontal plane $zequals;k$ with the surface defined by f. Level curves are also known as contour lines.
A vertical cross section (parallel to a coordinate plane) of a surface $zequals;f\left(xcomma;y\right)$ is a twodimensional curve with either the equation $zequals;f\left(ccomma;y\right)$ or the equation $zequals;f\left(xcomma;d\right)$, where c and d are constants. Such a cross section can be described as the intersection of a vertical plane $xequals;c$ or $yequals;d$ with the surface defined by f.
Both level curves and cross sections are helpful for visualizing and plotting multivariate functions.



Select a function from the dropdown menu or type your own function in the text box below and click "Enter" to plot it. Click the radio buttons to view either a level curve or a cross section. Use the slider to change the value of the related constant $k$, $c$, or $d$. Click "Reset" to reset both plots.

z = f(x, y) =





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