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Given a triangle ABC (ax, ay, bx, by, cx, cy) that may be rotated any which way about the origin and a point P (px, py), determine
whether or not P is in the Steiner Circum Ellipse for triangle ABC limited to Trigonometry and using as little steps as possible.
Retrieve the coordinates for both foci and the major/minor axes extrema relative to centroid g of triangle abc and graph the
ellipse using the standard equation for an ellipse.
Where
Q = a^2+b^2+c^2-ab-ac-bc
Sw = (a^2+b^2+c^2)/2
a (major axis) = 2/9*SquareRoot(Q+Sw)
b (minor axis) = 2/9*SquareRoot(Q-Sw)
c (foci) = 2/3*SquareRoot(Q)
(x-h)^2/a^2+(y-k)^2/b^2 = 1
whether or not P is in the Steiner Circum Ellipse for triangle ABC limited to Trigonometry and using as little steps as possible.
Retrieve the coordinates for both foci and the major/minor axes extrema relative to centroid g of triangle abc and graph the
ellipse using the standard equation for an ellipse.
Where
Q = a^2+b^2+c^2-ab-ac-bc
Sw = (a^2+b^2+c^2)/2
a (major axis) = 2/9*SquareRoot(Q+Sw)
b (minor axis) = 2/9*SquareRoot(Q-Sw)
c (foci) = 2/3*SquareRoot(Q)
(x-h)^2/a^2+(y-k)^2/b^2 = 1