This is not sufficient, however. While nine points determine a cubic, there are configurations of nine points that are special with respect to cubics, namely the intersection of two cubics. The intersection of two cubics, which is formula_1 points (by Bézout's theorem), is special in that nine points in general position are contained in a "unique" cubic, while if they are contained in two cubics they in fact are contained in a pencil (1-parameter linear system) of cubics, whose equations are the projective linear combinations of the equations for the two cubics. Thus such sets of points impose one fewer condition on cubics containing them than expected, and accordingly satisfy an additional constraint, namely the Cayley–Bacharach theorem that any cubic that contains eight of the points necessarily contains the ninth. Analogous statements hold for higher degree.