Hyperbola can be Drawn through Four Non-Collinear Points

Theorem

Let $A, B, C, D$ be points in the plane of which no $3$ are collinear.

Then a hyperbola can be drawn so that it passes through all points $A, B, C, D$.


Proof


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Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4$
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