Hyperbolic Function with Asymmetric Asymptotes

  • Thread starter hadron23
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  • #1
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Hello,

I wish to find a function similar to,

[itex]y^2-x^2=1[/itex]

but instead of the slope of the asymptotes being +/- 1, I need one of the asymptotes to be of slope 0. That is, I wish to find a hyperbolic function with one horizontal asymptote and the other of slope 1.

Is this possible?
 

Answers and Replies

  • #2
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I suppose all hyperbolas have asymptotes of equal slope magnitude but opposite sign, since they can just be thought of as a vertical conic cross section.

The function I am after essentially has to look like exp(x) for negative x and be linear for positive x. Think of an exponential function with a positive linear asymptote. I was hoping a hyperbolic function may be able to do this, but I don't believe it will. Any ideas?
 
  • #3
LCKurtz
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Do you know how to write the equation of a hyperbola aligned with the xy axes, centered at the origin whose asymptotes are lines through the origin with slope ±pi/8 and with intercepts on the y axis? If so, then rotate the graph by pi/8 and you will have your equation. Besides the x2 and y2 term you will also have an xy term in your answer.
 
  • #4
LCKurtz
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If you are still here, think about this much simpler equation:

[tex]xy - y^2 = -k^2[/tex]

The value of k will determine the y intercept.
 

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