How to choose the correct area to fill using build cycle in asymptote for strophoid?

Question

I had asked this question earlier here How to choose the correct area to fill using buildcycle in asymptote? and got the correct answer from Thruston. I have run into a similar problem, this time with a strophoid instead of ellipse.

 `/* Geogebra to Asymptote conversion, documentation at artofproblemsolving.com/Wiki go to User:Azjps/geogebra */
import contour; import graph; size(7cm); 
import patterns;
add("hatch",hatch(2.5mm));
string blank(real x) {return "";} 
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ 
pen dotstyle = black; /* point style */ 
real xmin = -5.5, xmax = 6.86, ymin = -6, ymax = 6.9;  /* image dimensions */

Label laxis; laxis.p = fontsize(10); 
xaxis(-5.5, xmax, Ticks(laxis,blank, Step = 1, Size = 2, NoZero),EndArrow(6), above = true); 
yaxis(-6.5, ymax, Ticks(laxis, blank, Step = 1, Size = 2, NoZero),EndArrow(6), above = true); /* draws axes; NoZero hides '0' label */ 
 /* draw figures */
real implicitf1 (real x, real y) { return (5.0+x)*y^2-x^2*(5.0-x); } 
guide[][] cf=contour(implicitf1, (xmin,ymin), (xmax,ymax), new real[]{0}, 500);
draw(cf[0][0], linewidth(1)); 
path p1=(5,1.5) -- (0,-6); 
draw(p1,linewidth(1));
path p2=buildcycle(p1,cf[0][0]);
fill(p2,pattern("hatch"));
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); 
 /* end of picture */`

Here is the resulting image. I want the other part to be shaded. Can anyone explain how buildcycle works?

Answer 1

I finally settled for the following:

import contour; import graph; size(7cm); 
import patterns;
add("hatch",hatch(2.5mm));
string blank(real x) {return "";} 
real labelscalefactor = 0.5; /* changes label-to-point distance */
pen dps = linewidth(0.7) + fontsize(10); defaultpen(dps); /* default pen style */ 
pen dotstyle = black; /* point style */ 
real xmin = -5.5, xmax = 6.86, ymin = -6, ymax = 6.9;  /* image dimensions */

Label laxis; laxis.p = fontsize(10); 
xaxis(-5.5, xmax, Ticks(laxis,blank, Step = 1, Size = 2, NoZero),EndArrow(6), above = true); 
yaxis(-6.5, ymax, Ticks(laxis, blank, Step = 1, Size = 2, NoZero),EndArrow(6), above = true); /* draws axes; NoZero hides '0' label */ 
 /* draw figures */
real implicitf1 (real x, real y) { return (5.0+x)*y^2-x^2*(5.0-x); } 
guide[][] cf=contour(implicitf1, (xmin,ymin), (xmax,ymax), new real[]{0}, 500);
draw(cf[0][0], linewidth(1)); 
real f1(real x){ return sqrt((x^2*(5-x))/(5.0+x));}
real f2(real x){ return -sqrt((x^2*(5-x))/(5.0+x));}
fill(graph(f1,0,4.61) -- (3,-1.5) -- graph(f2,3,0)-- cycle,pattern("hatch"));
path p1=(0,-6) -- (5,1.5); 
draw(p1,linewidth(1));
dot((4.61,0.92),linewidth(4)+dotstyle);
label("$A$",(4.7,0.94),E*labelscalefactor);
label("$B$",(3,-1.6),S*labelscalefactor);
dot((3,-1.5),linewidth(4)+dotstyle);
clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); 
 /* end of picture */

I get the following picture (What I want.): Of course I can draw the curve without using contour. Still, it will be nice, if there is a solution using asymptote. Asymptote documentation assumes that one is familiar with metapost documentation. So, it seems that one needs to dig into metapost documentation if we want to understand buildcycle better.