3

Part of 1992 Flanders Math Olympiad

Problems(1)

sphere and conic

Source: flanders '92

a conic with apotheme 1 slides (varying height and radius, with

r < \frac12

) so that the conic's area is

9

times that of its inscribed sphere. What's the height of that conic?

geometry3D geometrysphereconics