Level Curve

If a function z = f (x,y) is assigned to a value c, i.e. f (x,y) = c, then the curve f (x,y) = c is named as the level curve of f. 

If you take a look at the graph below, there is a paraboloid z = 10 - x² - y² at the right. By default, the choice of 'Show level curve z = 6' is ticked. The surface is 'cut' through by the plane z = 6 and the intersection yields the circle x² + y² = 4.

The circle is then drawn on the xy-plane at both columns. The circle on the xy-plane is the level curve.

Choose different level of c and observe the changes on level curves. Click here if you want to rotate the 3D graph.

Betty, created with GeoGebra and Thomas' Calculus, Pearson.