prologues := 3;
outputtemplate := "%j/%j-%c.svg";
outputformat := "svg";

verbatimtex
%&latex
\documentclass{minimal}
\usepackage[charter]{mathdesign}
\begin{document}
etex
% unitee
u:=.7cm;

%% Macro JMS -----------------------------------------------------------------
picture UnBeauPoint;
UnBeauPoint := image(
  fill fullcircle scaled 3pt;
fill fullcircle scaled 2pt withcolor white;
);
vardef pointe expr p = draw UnBeauPoint shifted p; enddef;
%%----------------------------------------------------------------------------

%parametre(s)
a:=3u;
%les points fixes
pair A,B,O;
O:=(0,0);
A:=(a,0);
%les points mobiles
pair C,P,D,M,N;
%le chemin du cadre de l'animation
pair cadre[];
cadre[0]:=(-4u,-8u);
cadre[1]:=(10u,-8u);
cadre[2]:=(10u,8u);
cadre[3]:=(-4u,8u);
%les chemins necessaires
path verticale, conchoideG, conchoideD,rayon;
verticale:=(a,2.8*ypart(cadre[1]))--(a,2.8*ypart(cadre[3]));
picture fond[];
l:=0; %compteur fond
j:=0; %compteur image

for b:=.2u step 0.04u until 5u:
  for k:=0 upto 1:
    B:=(a+b,0);
    if k=0:
      beginfig(j);
    else:
      beginfig(240-j);
    fi;
  %les axes
    drawarrow (xpart(cadre[0]),0)--(xpart(cadre[1]),0);
    drawarrow (0,ypart(cadre[1]))--(0,ypart(cadre[3]));
    draw verticale dashed evenly;
    if l>0:
      for m:=1 upto l:
        draw fond[m];
      endfor;
    fi;
  %le rayon
  % % un point du cercle unite
    for i:=80  step (-0.5) until -80:
      C:=(cosd(i),sind(i))*u;
      D:=25[O,C]; %le point D assez loin :-)
  %on dessine le rayon
      rayon:=O--D;
  %on determine P
      P:=verticale intersectionpoint rayon;
  %les points de la courbe
  % % on recupere la longueur OP
      long:=arclength(O--P);
      M:= (1-b/long)[O,P];
      N:= (1+b/long)[O,P];
  %les courbes
      if i=80:
        conchoideG:=M;
        conchoideD:=N;
      else:
        conchoideG:=conchoideG--M;
        conchoideD:=conchoideD--N;
      fi;
    endfor;
  %on dessine
    if (j mod 4)=0:
      l:=l+1;
      fond[l]:=image(
          draw conchoideG withcolor 0.8white withpen pencircle scaled 1pt;
        draw conchoideD withcolor 0.8white withpen pencircle scaled 1pt;
        );
    fi;
    draw conchoideG withcolor red withpen pencircle scaled 1pt;
    draw conchoideD withcolor red withpen pencircle scaled 1pt;
  % %on dessine les points fixes
    label.lrt(btex $A$ etex,A);
    label.lrt(btex $O$ etex,O);
    label.lrt(btex $B$ etex,B);
    pointe(B);
    pointe(A);
    pointe(O);
  %titre legende
    label(btex $\rho=\frac{a}{\cos \theta}\pm b$ etex, (8u,6u));
    label.lft(btex $a=3$ etex , (8.3u,-5u));
    label.lft(btex $b=$ etex ,(8u,-6u));
    label.rt((decimal (b/u)),(8u,-6u));
  %on clip
    clip currentpicture to cadre[0]--cadre[1]--cadre[2]--cadre[3]--cycle;
    draw cadre[0]--cadre[1]--cadre[2]--cadre[3]--cycle withcolor white;
  endfig;
endfor;
j:=j+1;
endfor;

end.