I was going through some properties a ellipses and this question comes to my mind: Suppose you have an ellipse on paper with nothing marked on it and for some reason you need to find the foci. How can you do that with just a pencil and a compass? Can we do that using this property: "The portion of a tangent to an ellipse between the point of contact and the directrix subtends a right angle at the corresponding focus." ?
2026-05-04 15:47:24.1777909644
Geometry of an ellipse
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Assuming you want a ruler and compass construction, there is a nice sequence at http://whistleralley.com/conics/conic_construction/ellipse_parts/. It shows how to find the center (via conjugate diameters), followed by the axes and then the foci.