Points Defined by Adjacent Pairs of Digits of Reciprocal of 13 lie on Hyperbola

Theorem
Consider the digits that form the recurring part of the reciprocal of $13$:
 * $\dfrac 1 {13} = 0 \cdotp \dot 07692 \dot 3$

Take the digits in ordered pairs, and treat them as coordinates of a Cartesian plane.

It will be found that they all lie on a hyperbola:


 * HyperbolaFromThirteenth.png

Proof

 * HyperbolaFromThirteenthSolution.png

Let the points be labelled to simplify:
 * $A := \left({0, 7}\right)$
 * $B := \left({7, 6}\right)$
 * $C := \left({6, 9}\right)$
 * $D := \left({9, 2}\right)$
 * $E := \left({2, 3}\right)$
 * $F := \left({3, 0}\right)$