The Maclaurin-Bézout 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 
.
Maclaurin-Bézout Theorem
See also
Cramér-Euler ParadoxExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Maclaurin-Bézout Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Maclaurin-BezoutTheorem.html