\documentclass[pstricks]{standalone}
\usepackage{pst-contourplot,multido,pst-math}
\begin{document}
\begin{pspicture}[showgrid](-4,-4)(8,4)
\pstVerb{/ai 2 def}%
\psset{a=0.1}% ncell=150 80,
\multido{\n=-3.50+0.25,\r=0+0.0476}{21}{
\definecolor{Descartes}{hsb}{\r\space 1 1}
\psContourPlot[linecolor=Descartes,function=
              -0.75 x dup mul y dup mul add sqrt mul
              1.25 x ai sub dup mul y dup mul add sqrt mul add
              \n\space add](-4,-4)(8,4)}
\psline{<->}(0,4)(0,0)(8,0)
\uput[d](0,0){$O_1$}
\uput[l](0,3.75){$y$}
\uput[u](7.9,0){$x$}
\psdots(!ai 0)(0,0)
\uput[d](!ai 0){$O_2$}
\end{pspicture}

\begin{pspicture}[showgrid=false](-4,-4)(8,4)
\pstVerb{/ai 2 def}%
\psset{a=0.1}
\multido{\n=-3.50+0.25,\r=0+0.0476}{21}{
\definecolor{Descartes}{hsb}{\r\space 1 1}
\psContourPlot[linecolor=Descartes,fillcolor=Descartes,Fill,
              function=
              -0.75 x dup mul y dup mul add sqrt mul
              1.25 x ai sub dup mul y dup mul add sqrt mul add
              \n\space add](-4,-4)(8,4)}
\end{pspicture}

\begin{pspicture}(-5,-5)(5,5)
\psframe*[linecolor=cyan](-5,-5)(5,5)
\psset{unit=0.5}%
\psContourPlot[linecolor=red,Fill,fillcolor=yellow,ReverseColors,a=0.05,function=x SIN y SIN 1 sub mul y SIN mul x SIN 1 sub mul](-10,-10)(10,10)
\end{pspicture}

\begin{pspicture}(-6.28,-6.28)(6.28,6.28)
% http://www.ensiie.fr/~gacogne/courbes.pdf
\psframe*[linecolor=cyan](-6.28,-6.28)(6.28,6.28)
\psset{unit=0.5}%
\psContourPlot[a=0.05,linecolor=red,Fill,fillcolor=yellow,ReverseColors,
              function=y SIN x COS mul x SIN sub
              x SIN y COS mul y SIN sub mul](-12.57,-12.57)(12.57,12.57)
\end{pspicture}
\end{document}