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Verification of a parabola

  1. Aug 25, 2005 #1
    I would like to verify my answer please:
    x^2-2xy+y^2+5x+5y=0

    using the formulas b^2-4ac=0 (indicates a parabola)
    b^2-4ac<0 (indicates an ellipse)
    b^2-4ac>0 (indicates a hyperbola)

    2^2-4(1)(1)=0
    4-4=0 therefore this graph must be a parabola!

    Am I correct?
     
  2. jcsd
  3. Aug 25, 2005 #2

    TD

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    It's indeed a parabola :smile:
     
  4. Aug 25, 2005 #3
    YIPPEE, thank
     
  5. Aug 25, 2005 #4

    arildno

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    Dearly Missed

    Note that your equation may be re-written as:
    [tex](x-y)^{2}+5(x+y)=0[/tex]
    This can be brought onto the form:
    [tex]u=-\frac{\sqrt{2}}{5}v^{2}, u=\frac{x+y}{\sqrt{2}}, v=\frac{x-y}{\sqrt{2}}[/tex]
    where the u-v axes are 45 degrees rotated with respect to the xy axes.
     
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