I'm having problems with this exercise:
For which points $P\in C$ ($C$ is a non-singular cubic) there exists a non-singular conic $Q$ with $C\cap Q = P$?
Maybe we can use Pappus' theorem or some other application of Noether's theorem?
Any ideas?
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To help people who might like to think about your question, can you give us some context? In particular, where is this exercise taken from? – Nov 01 '13 at 13:30
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Fulton's book, algebraic curves. – Mathematics Nov 01 '13 at 13:37