PUMaC 2008 Geometry B Problem 9

Let \mathcal{H} be the region of points (x, y), such that (1,0),(x, y),(-x, y), and (-1,0) form an isosceles trapezoid whose legs are shorter than the base between (x, y) and (-x, y). Find the least possible positive slope that a line could have without intersecting \mathcal{H}.