Marking areas in a graph

Question

Suppose I want to mark the area defined by the following equation:

$$\max(\mid x_1-a \mid,\mid x_2-b \mid) \leq c$$

for any real constants $a$, $b$, and $c$.

How do I do that in Mathematica? I can draw the border for the area by using the ContourPlot and and changing the inequality sign to an equality sign, but is there a way I can mark the area?

The above equation is just an example. In general, I am looking for a solution to mark the area given by any implicit function of the form $f(x_1,x_2) \leq c$ for a real constant $c$.

Answer 1

a = 5;
b = 10;
c = 7;
RegionPlot[
 Max[Abs[x - a], Abs[y - b]] <= c, 
 {x, -20, 20}, 
 {y, -20, 20}]