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I had a question that I cant seem to find an answer too.

I was hoping people could point me in the right direction, or let me know if there is an "easy" method.

It has to do with the classic example of two stones in water producing constructive and destructive interference patterns, which create a hyperbola.

If we are given the closest hyperbola created by the interference patterns. Is there an "easy" way...to generate the equations for the other hyperbola that are also created?

Generally I have just been plotting some circles and "guessing" at the other ones. However it seems like there should be a pretty easy method...since they all have the same focus right?

For example, I am trying to create the other hyperbolic arcs created at the same time is this mildly complex hyperbola:

[itex]y^2 = 4x^2 + 5x +632378[/itex]

Here is the wolframalpha of the equation:

http://www.wolframalpha.com/input/?i=y^2+=+4*x^2++5*x++632378

I would appreciate any feedback. Thank you!