6xy = 13color(white)("XXX")rArrcolor(white)("XXX")xy=13/6
As noted in the answer (above) neither x nor y can equal 0 (rArr the asymptotes are the X and Y axes).
The points on the curves closest to the origin will occur when x=y
color(white)("XXX")rArr at (sqrt(13/6),sqrt(13/6)) and (-sqrt(13/6),-sqrt(13/6))
color(white)("XXXXXXXXXXXXXXXXXXX")Note: sqrt(13/6) is approximately 1.47
It is difficult to find "nice" (i.e. integer) points to plot.
However note that x and y are symmetric. If (a,b) is a solution pair, then so are (b,a), (-a,-b), and (-b,-a)
color(white)("XXX"){:
(a," ",b),
(1," ", 2 1/6),
(2," ",1 1/12),
(3," ",13/18)
:}
graph{6xy = 13 [-5.546, 5.55, -2.78, 2.77]}
