The above definition, slightly altered, should work fine with lists …
catenary-20180119.dyn (6.5 KB)
l=Line.ByStartPointEndPoint(p1,p2);
x=(-l.Length/2)..(l.Length/2)..0.1;
z=a*Math.Cosh(x/a);
p3=Point.ByCoordinates(x,0,z);
p4=p3.Translate(Vector.ZAxis(),-List.FirstItem(p3<1>).Z);
or=l.PointAtParameter(0.5);
vx=Vector.ByTwoPoints(or,l.PointAtParameter(1));
vy=Vector.ByTwoPoints(or,or.Translate(Vector.YAxis(),1));
cs=CoordinateSystem.ByOriginVectors(or,vx,vy);
p5=p4.Transform(cs);