The easiest way will likely depend on the asymptote
code that you have already written. If you don't care about the exact angles of the cut, then you could create a subpath
of a section of the ellipse like so.
unitsize(1inch);
real a = 1.0;
real b = 0.8;
pair f = (sqrt(a*a - b*b), 0);
path ell = scale(a,b)*unitcircle;
path sector = subpath(ell, 2.5, 2.9);
filldraw(sector--f--cycle, yellow);
draw(ell);
draw(sector, 1+red);
dot(f, 6+red);

If you want to specify exact angles for the sector, then you can intersect
the ellipse with a rays shooting from the focus at the desired angles.
unitsize(1inch);
real a = 1.0;
real b = 0.8;
pair f = (sqrt(a*a - b*b), 0);
real angle1 = 90;
real angle2 = 180;
path ell = scale(a,b)*unitcircle;
path sector = subpath(ell,
intersect(ell, f--f+rotate(angle1)*(10,0))[0],
intersect(ell, f--f+rotate(angle2)*(10,0))[0]);
filldraw(sector--f--cycle, yellow);
draw(ell);
draw(sector, 1+red);
dot(f, 6+red);
