The conic (d) is a generalization of the Euler Circle of a triangle. The configuration here corresponds to the three vertices of the triangle plus its orthocenter as fourth point. In that case all the conics (c) are rectangular hyperbolas and their centers lie on the Euler circle of the triangle (see OrthoRectangular.html ).

In the general case, if q is non convex, then all conics (c) are hyperbolas and (d) is an ellipse. If q is convex then (d) is a hyperbola and the branch of (d) passing through the diagonal points of q is the locus of centers of hyperbolas, the other branch being the locus of centers of ellipses.

To obtain all points of (d) it suffices to consider all the conics passing through the four points {A

[AubertPapelier] Aubert, P & Papelier, G.

EulerCircleProperty.html

FourEulerCircles.html

HyperbolaRectangular.html

OrthoRectangular.html

RectHypeCircumscribed.html

RectHypeThroughFourPts.html

Symmetric_triangles2.html

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