Question 144212
Yes, it is a hyperbola that is symmetric to the line y=x.
If you plot a few points in the 1st and 3rd quadrants you
will see it..
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Since xy = 4/9 you can see that as x gets larger y has to get smaller 
but never gets to y=0 (the x-axis), and as y gets larger the x gets
smaller but never gets to x = 0 (the y-axis).  So the asymptotes are
the x and y axes.
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Cheers,
Stan H.