# 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

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 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(8909)   (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 aČ=16 and bČ=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