PUMaC 2024 · 几何（A 组） · 第 8 题

PUMaC 2024 — Geometry (Division A) — Problem 8

Let E be the ellipse lying in the x, y plane centered at (0 , 0) with semi-major axis of length 2 along the x -axis and semi-minor axis of length 1 along the y -axis. Let C be a cone created by revolving two perpendicular lines about an angle bisector of the perpendicular angle. There are some points ( x, y, z ) where the vertex of C could be so that E is the intersection of C with the x, y plane. These points define a convex polygon in the x, z plane. The area of this √ polygon can be expressed as n for some positive integer n . Find n . (Some definitions: the semi-major axis is the longest distance from the center of the ellipse to the boundary, and the semi-minor axis is the shortest distance from the center of the ellipse to the boundary.) Name: Team: Write answers in table below: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 2

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