# Thread: Practical application of a rational function with a parabolic Does asymptote?

1. ## Practical application of a rational function with a parabolic Does asymptote?

Does anyone know of any real-world situations (in science, engineering, etc) where a parabolic (or otherwise curvilinear) asymptote comes into relevance?

Thanks...

2. ## Re: Practical application of a rational function with a parabolic Does asymptote?

Here's one: when a string hangs under its own weight it forms a catenery, which is a constant times the hyperbolic cosine: $\displaystyle y = \frac A 2 (e^x + e^{-x})$. For large values of x this assymptotically approaches $\displaystyle y = \frac A 2 e^x$.

3. ## Re: Practical application of a rational function with a parabolic Does asymptote?

Thanks so much, ebaines.

4. ## Re: Practical application of a rational function with a parabolic Does asymptote?

Would you please clarify what variables x and y represent in this situation?

5. ## Re: Practical application of a rational function with a parabolic Does asymptote?

y= deflection of the string, and x = position along the horizontal axis, where x=0 is at the midpoint of the string. See the attached figure - the blue line is the hangng string and the red line is the graph of (1/2)e^x.

6. ## Re: Practical application of a rational function with a parabolic Does asymptote?

Does the constant A represent the length of the string?

7. ## Re: Practical application of a rational function with a parabolic Does asymptote?

Also, I've found several websites that present it this way:

$\displaystyle y = \frac{A}{2} \left( e^{x/a} + e^{-x/a} \right)$

Is this what you meant, or is this something different?