One-seventh ellipse

Fun fact. It is well known that
[tex] \frac{1}{7} = 0.\overline{142857} [/tex].

It turns out that if the repeating digits are taken in sequence as (x,y) pairs in the following manner to form six points:
(1,4), (4,2), (2,8), (8,5), (5,7), (7,1),
then these six points actually lie on an ellipse defined by the following equation.
[tex] 19x^2+36xy+41y^2-333x-531y+1638=0 [/tex]

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