# ParametricPlot with condition for parameters

For example

ParametricPlot[{Sin[x] - y, Cos[y] - x}, {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}]


gives

What should I do to impose x^2+y^2==2 (actually it could be a more complicated function) and only plot for those parameters that satisfy that condition? Mesh didnt work.

 Quiet @ ParametricPlot[{Sin[x] - y, Cos[y] - x} , {x, -π, π}, {y, -π, π},

Use BoundaryStyle -> None and PlotStyle -> None to hide the surface and its boundary.