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The locus of the center of circumscribed conics. (a) The locus of the center of circumscribed conics of a convex quadrilateral is its nine-point curve, which is a hyperbola. (b) The axes of symmetry of a general convex quadrilateral’s two circumscribed parabolas are parallel to the asymptotic lines of its nine-point curve, respectively. (c) The center 0 of the circumscribed conics of a concave quadrilateral is on its nine-point curve, which is an ellipse.
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The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the...
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