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Identifying similar families of cuvers

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data

    State which of the following families of curves are similar sets.

    2. Relevant equations

    1)Y[itex]^{2}[/itex]=4ax
    2)Y=acosh([itex]\frac{x}{a}[/itex])
    3)[itex]\frac{x^{2}}{a^{2}}[/itex]+[itex]\frac{y^{2}}{b^{2}}[/itex]=1
    4)Y=2a[itex]^{3}[/itex]log[itex]\frac{x}{a^{3}}[/itex]
    5)btan[itex]^{-1}[/itex][itex]\frac{y}{x}[/itex]=a+y
    6)x[itex]^{3}[/itex]+y[itex]^{3}[/itex]=3axy

    3. The attempt at a solution

    1)parabola
    2)Parabola
    3)hyperbola
    4)I don't know which type of this curve is!
    5)I don't know which type of this curve is!
    6)this seems like circle. but in circle both terms x and y are squared and here is cube.

    Kindly tell me whether I am wrong in guessing families or not??
    Thanks
     
  2. jcsd
  3. Oct 13, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I am not sure what you mean by "similar" but only the first and third are conic sections- and the third is an ellipse, not a hyperbola. (2 "looks like" a parabola but is not.)
     
  4. Oct 13, 2011 #3
    Similar means like families.
    Ok yes 3rd one is ellipse. But what about 2,4,5 and 6. How to deduce the types of these curves? Any hint will be appreciable.
     
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