Bézout's Theorem/Examples/Conic Sections

Example of Use of Bézout's Theorem

Two conic sections meet in at most $4$ points.


Proof

From Conic Section is Curve of Second Degree, the degree of the polynomial defining a conic section is $2$.

Hence, by Bézout's Theorem two such conic sections meet in at most $2 \times 2 = 4$ points.

$\blacksquare$


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bézout's Theorem
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