SOLUTION: What is the shape of the graph: {{{x^2(x+y+1)=y^2(y+x+1)}}}

Algebra ->  Graphs -> SOLUTION: What is the shape of the graph: {{{x^2(x+y+1)=y^2(y+x+1)}}}      Log On


   

Question 1127779: What is the shape of the graph:
x%5E2%28x%2By%2B1%29=y%5E2%28y%2Bx%2B1%29
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the shape of the graph:
x%5E2%28x%2By%2B1%29=y%5E2%28y%2Bx%2B1%29
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x^2 = y^2 --> a degenerate hyperbola. 2 lines, slopes of -1 and +1 thru the Origin.
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Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.
x%5E2%28x%2By%2B1%29 = y%5E2%28y%2Bx%2B1%29  ====>


x%5E2%28x%2By%2B1%29 - y%5E2%28y%2Bx%2B1%29 = 0  ====>


%28x%5E2+-+y%5E2%29%2A%28x+%2B+y+%2B+1%29 = 0  ====>


(x - y)*(x + y)*(x + y + 1) = 0  ====>


This equation codes 3 (three, THREE) straight lines.


    1.  One equation is the straight line y = x.


    2.  Second equation is the straight line  y = -x.


    3.  Third equation is the straight line  y = -x - 1.

Solved.