Is an astroid made of arcs of ellipses?

ARCs astroid ellipses
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Is an astroid made of arcs of ellipses?

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Line segment AB, of constant length and with A on y-axis, models a ‘falling ladder’. The curve in red is the envelope of the supporting line, actually an astroid, apparently made of four parts, each being perhaps an arc of a circle or of an ellipse. We can easily disqualify an arc of a circle, simply by looking. We can then test whether an ellipse fits our curve using Cabri’s conic tool selecting five points on the locus. Apparently the fit is excellent. However, Cabri’s ‘Check Property’ feature proves that the fit is not exact: consider an additional point M on the locus and test its membership to the ellipse. Cabri reports that it is not.

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