You've probably seen this shape before. It is several straight lines whose outline seems to be curved. Connect the following pairs of points with segments:
(1,0) and (0,8)
(2,0) and (0,7)
(3,0) and (0,6)
(8,0) and (0,1)
The 8 segments seem to form the outline a curve, but what curve? Is it a circle or maybe one branch of a hyperbola? Some other conic? Does it's equation have some other nice form?