One way to get an informative picture is with ContourPlot
:
Show[ContourPlot[x^2 - y^2, {x, -2, 2}, {y, -2, 2}, Contours -> 20,
PlotPoints -> 50, ContourShading -> False, ContourStyle -> Black],
ContourPlot[x y, {x, -2, 2}, {y, -2, 2}, Contours -> 20,
PlotPoints -> 50, ContourShading -> False, ContourStyle -> Red]]
Disappointingly, this concise version shows only the 0
-level contours:
ContourPlot[{x^2 - y^2, x y}, {x, -2, 2}, {y, -2, 2},
Contours -> 20, ContourShading -> False]