path base; base = fullcircle rotated 180 scaled 2a shifted (2a, 0);
numeric s; s = 1/4;
pair A; A = 2[center base, point 0 of base];
path limacon; limacon = for t = 0 step s until length base:
A reflectedabout(precontrol t of base, postcontrol t of base) ..
endfor cycle;
path c[]; numeric n; n = -1;
for t = 0 step s until length base:
c[incr n] = fullcircle scaled 2 abs (point t of base - A) shifted point t of base;
draw c[n] withpen pencircle scaled 1/4 withcolor 3/4;
endfor
draw base withcolor 2/3 blue;
draw center base withpen pencircle scaled 2 withcolor 2/3 blue;
draw limacon withcolor 2/3 red;
dotlabel.lft("$A$", A);
dotlabel.urt("$Q$", point 5.4 of base);
dotlabel.ulft("$P$", A reflectedabout(precontrol 5.4 of base, postcontrol 5.4 of base));
endfig;
\end{mplibcode}
\end{document}
