SOLUTION: hello && greetings please help !! Which conic section is represented by the equation {{{4x^2-4xy+y^2+4x-2y+1=0}}} ???? A. ELLIPSE B. 2 LINES C. HYPERBOLA D. 1 LINE E. NON

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: hello && greetings please help !! Which conic section is represented by the equation {{{4x^2-4xy+y^2+4x-2y+1=0}}} ???? A. ELLIPSE B. 2 LINES C. HYPERBOLA D. 1 LINE E. NON      Log On


   

Question 146643: hello && greetings please help !!
Which conic section is represented by the equation 4x%5E2-4xy%2By%5E2%2B4x-2y%2B1=0 ????
A. ELLIPSE
B. 2 LINES
C. HYPERBOLA
D. 1 LINE
E. NONE OF THESE
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
hello && greetings please help !!
Which conic section is represented by the equation 4x%5E2-4xy%2By%5E2%2B4x-2y%2B1=0 ????
A. ELLIPSE
B. 2 LINES
C. HYPERBOLA
D. 1 LINE
E. NONE OF THESE 


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