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Classification of figure from the general equation of conics

  1. Jan 18, 2008 #1
    during my study on conics , I found a formula in the book regarding the classification of figure from the general equation of conics

    ax2+2hxy+by2+2gx+2fy+c=0

    it was given that
    [itex]\Delta=abc+2fgh-af^{2}-{bg}^{2}-{ch}^{2}[/itex]

    [itex]if \Delta \neq 0[/itex]
    then if
    [itex]h^{2}=ab.......parabola[/itex]
    [itex]h^{2}<ab......ellipse[/itex]
    [itex]h^{2}>ab.......hyperbola[/itex]

    if
    [itex]\Delta <0..........circle ,h=0,a=b\neq 0,g^{2}+f^{2}-ac>0[/itex]

    if
    [itex]\Delta = 0[/itex]
    if
    [tex]h^{2}>=ab..........line[/tex]
    [tex]h^{2}<ab..........unique point[/tex]



    No explanation regarding the derivation of result was given
    neither i could find it on net

    hope someone knows it........

    thanks in advance
     
    Last edited by a moderator: Mar 9, 2013
  2. jcsd
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