  In this note we study the limiting behaviour of the symbolic generic initial
system of an ideal I in K[x,y,z] corresponding to an arrangement of r points of
P2 lying on an irreducible conic. In particular, we show that the limiting
shape of this system is the subset of R2 such consisting of all points above
the line through (2,0) and (0, r/2) when r is greater than or equal to four.
