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Problem in conics

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data

    The equation ##x^2y^2-2xy^2-3y^2-4x^2y+8xy+12y=0## represents??

    2. Relevant equations

    circle: ##x^2 +y^2 = a^2##

    3. The attempt at a solution
    i know this has something to do with seperating out the variables but i dont seem to get the req equation
     
    Last edited: Jan 31, 2013
  2. jcsd
  3. Jan 31, 2013 #2

    Mark44

    Staff: Mentor

    Show us what you've tried.
     
  4. Jan 31, 2013 #3

    Dick

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    You want to try to factor it somehow. Why are there two xy terms in your expression? Check for typos.
     
  5. Jan 31, 2013 #4
    i divided the whole term by y^2 and i seperated the y and x terms on both sides of the equation then i think the next step would be to convert into factors but how am i supposed to do that why y would be in the denominator in rhs??
     
  6. Jan 31, 2013 #5
    sorry its ##xy^2##
     
  7. Jan 31, 2013 #6

    Dick

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    Ok, then start trying to factor it. You can pull a y out right away.
     
  8. Feb 1, 2013 #7
    ##x^2y^2−2xy^2−3y^2−4x^2y+8xy+12y=0##
    ##y^2(x^2-2x-3)-4y(x^2-2x-3)=0##
    ##y-4=0##
    ##y=4##??? what conic is that? is it a straight line :confused:
     
  9. Feb 1, 2013 #8

    Dick

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    Yes, it's a line. It can happen. xy=1 is a hyperbola. xy=0 is two lines. That's a 'degenerate conic'. But actually since your equation is 4th degree, there's not necessarily any reason to expect it to be a conic. But y=4 isn't the whole story.
     
    Last edited: Feb 1, 2013
  10. Feb 1, 2013 #9

    Mark44

    Staff: Mentor

    You skipped some steps here. Write the equation above as a product instead of a difference. In the two terms above there is a common factor: x2 - 2x - 3.
     
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