Hi Rick,

See the implementation of

17 x^2 - 16|x|y + 17 y^2 =225

in wolframalpha:
http://www.wolframalpha.com/input/?i=RegionPlot[17+x^2-16+Abs[x]+y+%2B17+y^2%3D225,{x,+-5,5},{y,-5,5}]

Recently I use wolframalpha heavily. Wonderful tool.