It is well known that through five points on a projective plane you can pass a conic.
Q. What happens when points collide ?
More precisely: if I consider a more simple question of two points and passing a line through them, then if I take a point in a Hilbert scheme of two points $Hilb^2$ I can pass exactly one line when this points collide.
Q Now, can I draw a conic (maybe singular) if I choose a point in $Hilb^5$ of projective plane? Or may be I need some different version of moduli space of points? The symmetric powers not work at all.