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Question 144212: hi
im a student who is struggling with conics
therefore i'll appreciate it if you could help me
i do not understand why this equation below is a "hyperbola" ... ?
my teacher said that it was a hyperbola and i still don't get it
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9xy = 4
i found that the standard form was y= 4/9x but why is this an hyperbola?
doesn't both x and y have to be squared??
and can you please tell me how to graph it??
i also learned that it has both horizontal and vertical asymptotes
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thank you so much for your help!
i'll be waiting
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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