Conic Section through Five Points

Theorem

Let $A, B, C, D, E$ be distinct points in the plane such that no $3$ of them are collinear.

Then it is possible to draw a conic section that passes through all $5$ points.


Proof


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Historical Note

The technique for constructing a conic section that passes through $5$ non-collinear points was demonstrated by Pappus of Alexandria.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
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