A curve of order is generally determined by points. So a Conic Section is determined by five points and a Cubic Curve should require nine. But the Maclaurin-Bezout Theorem says that two curves of degree intersect in points, so two Cubics intersect in nine points. This means that points do not always uniquely determine a single curve of order . The paradox was publicized by Stirling, and explained by Plücker.
See also Cubic Curve, Maclaurin-Bezout Theorem