Difference between Distances from Point on Hyperbola to Foci is Constant

Theorem

Let $K$ be a hyperbola.

Let $F_1$ and $F_2$ be the foci of $K$.

Let $P$ be an arbitrary point on $K$.

Then the distance from $P$ to $F_1$ minus the distance from $P$ to $F_2$ is constant for all $P$ on $K$.

Proof

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Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Problems for the Greeks