\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
path base; base = fullcircle scaled 300;
path astroid; astroid = for t=0 step 1/16 until 8:
hide(pair a, b, p;
a = (xpart point t of base, 0); b = (0, ypart point t of base);
p = whatever[a,b]; p - point t of base = whatever * (a-b) rotated 90;
) p -- endfor cycle;
for t=0 step 1/16 until 8:
draw (xpart point t of base, 0) -- (0, ypart point t of base) withcolor 7/8;
endfor
draw astroid withcolor 2/3 red;
endfig;
\end{mplibcode}
\end{document}