SOLUTION: Which of the following is an equation of one of the asymptotes of the hyperbola: 3x2-3y2=48? x-y=0 3x-3y=0 y-3x=0 x+27y=0

Question 373977: Which of the following is an equation of one of the asymptotes of the hyperbola:
3x2-3y2=48?
x-y=0
3x-3y=0
y-3x=0
x+27y=0

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Which of the following is an equation of one of the asymptotes of the hyperbola:

First we must get the equation in either the form or
. Either way we get a 1 on the right side by dividing every term
by 48.

Comparing to , we see that
a�=16 and b�=16 and so a=4, b=4
The defining rectangle is then:

So its extended diagonals are the asymptotes:

And they have slope �1 and pass through the origin so their equations are
y = x and y = -x
In standard form these are
x-y=0 and x+y=0
x-y=0 is one of the choices. But I notice that there is also
the choice 3x-3y=0, which is equivalent to x-y=0. So either
of these would technically be correct.
Edwin

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