SOLUTION: please help me which conic section is represented by the equation 4x^2-4xy+y^2+4x-2y+1=0 A.ellipse B.2lines C.hyperbola D.1 line E.n/a

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Question 146718: please help me
which conic section is represented by the equation 4x^2-4xy+y^2+4x-2y+1=0
A.ellipse
B.2lines
C.hyperbola
D.1 line
E.n/a
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
please help me
which conic section is represented by the equation 4x^2-4xy+y^2+4x-2y+1=0
A.ellipse
B.2lines
C.hyperbola
D.1 line
E.n/a


4x%5E2-4xy%2By%5E2%2B4x-2y%2B1=0 

Group the first three terms and
group the fourth and fifth terms:

%284x%5E2-4xy%2By%5E2%29%2B%284x-2y%29%2B1=0

Factor the trinomial in the first parentheses

%282x-y%29%282x-y%29%2B%284x-2y%29%2B1=0

Write %282x-y%29%282x-y%29 as %282x-y%29%5E2

%282x-y%29%5E2%2B%284x-2y%29%2B1=0

Factor 2 out of the second parentheses:

%282x-y%29%5E2%2B2%282x-y%29%2B1=0

Let z=%282x-y%29

z%5E2%2B2z%2B1=0

Factor that as

%28z%2B1%29%28z%2B1%29=0

%28z%2B1%29%5E2=0

Use the square root principle:

sqrt%28%28z%2B1%29%5E2%29=±sqrt%280%29

z%2B1=0

Since z=2x-y, replace z by 2x-y

2x-y%2B1=0

This the equation of one line:

So the correct choice is D

Edwin