Using a list to make a contour plot of multiple values

Question

I'm trying to make a contour plot for multiple values of the same function.

To accomplish that, I'm doing the following:

lst = Table[x^2 - y^2 == i, {i, -100, 100, 10} ]

ContourPlot[lst, {x,-10,10}, {y,-10,10}]

But it produces an empty plot (it's blank).

However, if I paste the contents of the list into the command, i.e.,

ContourPlot[
 {x^2 - y^2 == -100, x^2 - y^2 == -90, x^2 - y^2 == -80, 
 x^2 - y^2 == -70, x^2 - y^2 == -60, x^2 - y^2 == -50, 
 x^2 - y^2 == -40, x^2 - y^2 == -30, x^2 - y^2 == -20, 
 x^2 - y^2 == -10, x^2 - y^2 == 0, x^2 - y^2 == 10, x^2 - y^2 == 20, 
 x^2 - y^2 == 30, x^2 - y^2 == 40, x^2 - y^2 == 50, x^2 - y^2 == 60, 
 x^2 - y^2 == 70, x^2 - y^2 == 80, x^2 - y^2 == 90, x^2 - y^2 == 100},
 {x, -10, 10}, {y, -10, 10}]

it works.

What's is the difference between using lst, instead of the whole list within ContourPlot[].

Answer 1

You need to Evaluate the expression.

ContourPlot[Evaluate@lst, {x, -10, 10}, {y, -10, 10}]

Answer 2

We can use x^2 - y^2 as the first argument of ContourPlot with the option ContourShading -> None (as suggested by JM in comments) and get colored contours using the form $\{\{level_1, style_1\},\ldots\}$ for setting the option Contours:

levels = Range[-100, 100, 10];
colors = ColorData[97] /@ Range[21];

contours = Transpose[{levels, colors}]

ContourPlot[x^2 - y^2, {x, -10, 10}, {y, -10, 10}, 
 Contours -> contours, BaseStyle -> Thick, ContourShading -> None]