#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]}
