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## #1 2014-04-10 10:06:28

Reuel
Member
Registered: 2010-11-28
Posts: 178

### Determining the Vertex of a Hyperbola with Known Points

Hi!. Long time no post.

I have a question about finding the vertex of a hyperbola in elliptic coordinates. Suppose your coordinate system is given by

and suppose, somehow, you happen to know that a≠1 and you also happen to know a few of the points along the hyperbola... I don't know, maybe you have a diagram or something that shows the points labeled.

Does anyone know of a method for finding a≠1 based entirely on a few points along the hyperbola?

Thanks.

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## #2 2014-04-10 18:43:23

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,743

### Re: Determining the Vertex of a Hyperbola with Known Points

hi Reuel,

I would attempt to eliminate the parameter like this:

Write as

http://en.wikipedia.org/wiki/Hyperbolic_function

and similarly for y, and then evaluate

That will convert the equations to the more common format and make it easy to find a.  (I hope )

Bob

Last edited by bob bundy (2014-04-10 18:48:48)

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## #3 2014-04-11 01:12:52

Reuel
Member
Registered: 2010-11-28
Posts: 178

### Re: Determining the Vertex of a Hyperbola with Known Points

Nevermind, I've got it. You can use the very identity you suggested to set up a system of equations and solve for "a" that way.

Thanks for reminding me of that identity.

Last edited by Reuel (2014-04-11 01:42:54)

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