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Graph and Differential equations for hyperbolas

  1. Oct 11, 2011 #1
    Hello experts!
    Hope all of you will be fine.

    I have an equation i.e. xy=c
    And we all know it is hyperbola.

    Now I say "graph some of the hyperbolas xy=c". Then kindly tell me how can we extract more than 1 graph from this single equation? And you will write the differential equations for them. while here only 1 hyperbola is given i.e. xy=c.


    If you have any confusion about the question the kindly tell me. I will try to clear more.

    Thanks in advance.
     
  2. jcsd
  3. Oct 11, 2011 #2
    Assuming c is some constant, you have y = c/x. This is a family of graphs, which varies based on values of c. I.E. y = 1/x, y = 2/x, ...y = c/x
     
  4. Oct 13, 2011 #3
    Oh thanks. It is quite helpful.
     
  5. Oct 13, 2011 #4
    y[itex]^{2}[/itex]=4ax is also a parabola & and y=[itex]\frac{c}{x}[/itex] too?

    Is it?
     
  6. Oct 13, 2011 #5

    HallsofIvy

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    Yes, [itex]y^2= 4ax[/itex] would be a family of parabolas, all passing through (0, 0) having different foci.

    I'm not sure what your question about y= c/x is. It is the same as xy= c, your original hyperbola system.
     
  7. Oct 14, 2011 #6
    My real question as you can see that, how can you plot some hyperbolas families from general equation i.e. xy=c?

    This could be y=c/x and therefore some families will be y=1/x, y=2/x, y=3/x..........so on.
    Where c=any arbitrary constant.

    Am I right?
     
  8. Oct 14, 2011 #7

    HallsofIvy

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    Yes, that is exactly what it is saying. They will be parabolas having the x and y axes as asymptotes, passing through (1, c) and (-1, -c), for each number c. Be sure to include some values of c negative and c= 0.
     
  9. Oct 14, 2011 #8
    As you said c=0 this implies that y=0/x or y=0
    Can y=0 be a parabola? Is it so?
     
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