In[]:=
Manipulate[​​GraphicsRow[{​​f[x==y,{x,-3/2,3/2},{y,-3/2,3/2}],​​f[x^2+y^2==1,{x,-3/2,3/2},{y,-3/2,3/2}],​​f[xy==0,{x,-3/2,3/2},{y,-3/2,3/2}],​​f[x==0&&y==0,{x,-3/2,3/2},{y,-3/2,3/2}]​​}],​​{f,{ContourPlot,RegionPlot}}]
Out[]=
​
f
ContourPlot
RegionPlot