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

Algebra ->  Quadratic-relations-and-conic-sections -> 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       Log On


   

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) About Me  (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:

3x%5E2-3y%5E2=48
First we must get the equation in either the form x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1 or
y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1. Either way we get a 1 on the right side by dividing every term
by 48.
3x%5E2%2F48-3y%5E2%2F48=48%2F48
x%5E2%2F16-y%5E2%2F16=1
Comparing to x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1, 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