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X(2), X(291), X(350), X(447), X(519), X(903) points at infinity of the Steiner ellipses |
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K296 is an isotomic conico-pivotal isocubic. Its node is G with nodal tangents parallel to the asymptotes of the circum-conic (H) through G and X(7), the Gergonne point. It meets the Steiner circum-ellipse at infinity and at A, B, C, X(903). The real asymptote is the line X(190)-X(519). K296 is a member of the class CL031. It is also a tripolar centroidal cubic of the class CL045. The isogonal transform of K296 is K224. K296 is the transform of (H) under the Hirst transformation with pole G with respect to the Steiner circum-ellipse. In barycentric coordinates, this is the mapping (x : y : z)--> (x^2-yz : y^2-zx : z^2-xy). Hence, K296 contains all the images of the points of (H) under this transformation, most of them not mentioned in ETC. |
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