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?
I would attempt to eliminate the parameter like this:
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 )
Last edited by bob bundy (2014-04-10 18:48:48)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
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)