So when the plane intersect the cone, the intersection is a conic. Is (or when is) the axis (of the cone) intersection with the plane the focus of the conic?
2026-03-30 10:09:30.1774865370
intersection of cone axis with plane
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Just when the plane is orthogonal to the axis, since the focus lies on the Dandelin sphere that is tangent to the plane and the cone.