SOLUTION: Determine the nature of the following degenerate conics {{{x^2 + xy - 2y^2 + 3x + 6y = 0 }}}

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Question 1192204: Determine the nature of the following degenerate conics
x%5E2+%2B+xy+-+2y%5E2+%2B+3x+%2B+6y+=+0+
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Determine the nature of the following degenerate conics
x^2 + xy - 2y^2 + 3x + 6y = 0.
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

You may check that

    x^2 + xy - 2y^2 + 3x + 6y =(x + 2y) (x - y + 3).    (1)


So this formula is factoring the given polynomial of two variables into the product of two linear polynomials.


Thus the given original equation describes the union of two straight lines.



One straight line is

    x + 2y = 0         (2)


  
Other straight line is

    x - y + 3 = 0.     (3)

Solved.