SOLUTION: Asymptote questions (x+y)�(x+2y+2)-x-9y-2=0 x�+y�-3axy=0 y�(x�-a�)=x�(x�-4a�) x�-2y�+xy(2x-y) +y(x-1)+1=0 x�y�-a�(x�+y�)-a�(x+y)+a ki power 4 =0

Question 1023991: Asymptote questions
(x+y)�(x+2y+2)-x-9y-2=0
x�+y�-3axy=0
y�(x�-a�)=x�(x�-4a�)
x�-2y�+xy(2x-y) +y(x-1)+1=0
x�y�-a�(x�+y�)-a�(x+y)+a ki power 4 =0
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
We want to know the behavior of the function as x goes to and
a. Divide both sides of by . We get

Upon letting or , the equation becomes
.
Now let w = y/x.==> . Solving for w, we get w = -1 or w = -1/2. Hence the asymptotes are y = -x and y = -x/2.
b. . Divide both sides again by .
==> . As x goes to plus or minus infinity, the equation becomes .
==> . Let w = y/x, and so .
==> w = -1, or y/x = -1. Hence the asymptote is y = -x.
d.
Again divide both sides by .
The equation becomes . Letting x go to plus or minus infinity, the equation becomes
. Let y/x = w.
==> <==>
Solving for w, we get w = 1, -1, or -1/2.
Hence the asymptotes are y = x, y = -x, and y = -x/2.
I leave parts c and d to you.
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