Difference between Distances from Point on Hyperbola to Foci is Constant

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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


Sources