asympt01

\begin{asy}
// file fod.asy
//
// to get fod.pdf, run `asy -f pdf fod.asy`
//
size(8cm);
import graph;
import fontsize;
defaultpen(fontsize(9pt));

texpreamble("\usepackage{lmodern}");

pen curvepen=darkblue+0.8bp;
pen linepen=darkred+0.8bp;
pen fillpen=orange+opacity(0.5);

real
xmin=-20, xmax=-xmin,
ymin=-20, ymax=-ymin;

xaxis(xmin,xmax,RightTicks(Step=10,step=5,OmitTick(0)));
yaxis(ymin,ymax, LeftTicks(Step=10,step=5,OmitTick(0)));

real a=10;

real r(real t){return 3*a*sin(t)*cos(t)/(sin(t)^3+cos(t)^3);};

real tmin=-0.16pi, tmax=pi/2-tmin;

guide
loop=polargraph(r,0,pi/2)--cycle,
curve=polargraph(r,tmin,tmax);

fill(loop, fillpen);
draw(curve,curvepen);

pair
p=point(curve,0),
q=point(curve,length(curve));

draw((p.x,-p.x-a)--(-q.y-a,q.y),linepen);
\end{asy}