/*<asyxml>syracuse</asyxml>*/
import geometry_dev;
import animate;
// settings.tex="pdflatex";
// settings.outformat="pdf";

animation anim;
size(12cm);


ellipse ellipse(point F1, real a, real c, point tgt, vector dir)
{
  line d=line(tgt,tgt+dir);
  line bis=perpendicular(tgt,d);
  line l=line(tgt,reflect(bis)*F1);
  point[] F=intersectionpoints(circle(F1,2*c),l);
  real a0=abs(F1-tgt)+abs(F[0]-tgt);
  real a1=F.length > 1 ? abs(F1-tgt)+abs(F[1]-tgt) : 0;
  return abs(a0/2-a) < 1e-5 ? ellipse(F1,F[0],a0/2) : ellipse(F1,F[1],a1/2);
}

point F1=(0,0), F2=(0,-3);
dot("F",F1);

ellipse el1=ellipse(F1,F2,2), el2;
point Fp1=shift(0,2*el1.a)*F1;
dot("F'",Fp1);

line tgt, saxe=line(F1,false,-F2);

for (int i=0; i < 360; i += 5) {
  save();
  ellipse el=rotate(i,F1)*el1;
  point M=intersectionpoints(el,saxe)[0];
  tgt=tangents(el,M)[0];
  draw(tgt, 0.8*red);
  el2=ellipse(Fp1,el1.a,el1.c,M,tgt.u);
  draw(el2^^el, linewidth(bp));
  anim.add();
  restore();
}
erase();
anim.movie();