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analytical geometry

Source: flanders '97

September 27, 2005
geometryfunctiontrigonometryanalytic geometry

Problem Statement

In the cartesian plane, consider the curves x2+y2=r2x^2+y^2=r^2 and (xy)2=1(xy)^2=1. Call FrF_r the convex polygon with vertices the points of intersection of these 2 curves. (if they exist) (a) Find the area of the polygon as a function of rr. (b) For which values of rr do we have a regular polygon?
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