The CPC or compound parabolic concentrator uses two parabolas that are rotated relative to one another to accept all light within a certain 'angle of acceptance' and deliver that light to the outlet, which is smaller than the inlet by a concentration factor. The parabolas are rotated w.r.t one another - if possible i'd like to find a method using string and ruler or the like as in the links below - no math.
There are easy ways to construct parabolas like this or
For use with tubular collectors: CPC tube setup
I think the main conceptual problem has been solved. In the pages above there seems to be an implication that the input area, output area, and distance between these are arbitrary. But it seems to me that two of the three determine the third ; as a check I chose all three arbitrary and indeed this leads to a miss - see below.