2007 Putnam A2

Find the least possible area of a convex set in the plane that

intersects both branches of the hyperbola $xy = 1$ and both branches of

the hyperbola $xy = -1$. (A set $S$ in the plane is called *convex*

if for any two points in $S$ the line segment connecting them is

contained in $S$.)

求平面上凸集的最小可能面积

与双曲线的两个分支 $xy = 1$ 相交，并且与

双曲线 $xy = -1$。 (平面上的集合$S$称为*凸*

如果对于 $S$ 中的任意两点，连接它们的线段是

包含在 $S$ 中。)