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Asymptotes for hyperbolas q2 problem :S

  1. Aug 12, 2006 #1
    Does the equation (x+1)^2-4y^2 = 0 have asymptotote??
    i graphed it and from the graph it does not look like a hyperbola because it seems to intersect at the point x = -1 y = 0 :frown:


    Thanks HallsofIvy for helpin me with the previous asymptote hyperbola prob
     
  2. jcsd
  3. Aug 13, 2006 #2
    The equation you wrote doesn't describe a hyperbola but two straight lines intersecting in the point (-1, 0). In fact you can write

    [tex](x+1)^2- 4 y^2 = 0 \Rightarrow (x +1 - 2 y) (x +1 + 2 y) =0[/tex]

    which implies

    [tex]x+1 -2y=0[/tex]

    or

    [tex]x + 1 + 2 y =0[/tex]

    (the stright line equations).

    If the equation was

    [tex](x+1)^2-4y^2=1[/tex]

    it described a hyperbola shifted back along the x-axis with vertex in (-1,0).
    The previously stright line equations are the asymptotes.
     
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