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January 11th, 2012, 03:52 PM  #1 
Member Joined: Dec 2011 Posts: 41 Thanks: 0  Ellipse question (eccentricity e.t.c)  pre exam
Let be the eccentricity and the focal parameter of an ellipse in the plane. Find such that the equation of the ellipse becomes Find the two focusdirectrix pairs. Direction on the directrix would be great cheers no but im pretty clueless on this all round so any help very much appreciated. 
January 11th, 2012, 06:11 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Ellipse question (eccentricity e.t.c)  pre exam
The focal parameter of an ellipse p is given by: The eccentricity e of an ellipse is given by: So we have the nonlinear system: (1) (2) We may arrange (2) as: We may arrange (1) as Thus Substituting for a into (2) gives: Since 0 < b, we may square: and so: Since a > b, the major axis is on the xaxis, and the foci will be at the points The directices will be the lines Note: the directrices may also be found with 
January 12th, 2012, 02:11 PM  #3 
Member Joined: Dec 2011 Posts: 41 Thanks: 0  Re: Ellipse question (eccentricity e.t.c)  pre exam
Thank you indeed. i will study what your post.

January 13th, 2012, 08:24 AM  #4 
Member Joined: Dec 2011 Posts: 41 Thanks: 0  Re: Ellipse question (eccentricity e.t.c)  pre exam
shockingly bad post by me. forgot to take out the what.

January 13th, 2012, 08:29 AM  #5 
Member Joined: Dec 2011 Posts: 41 Thanks: 0  Re: Ellipse question (eccentricity e.t.c)  pre exam
though im still a little unsure about the major axis on teh x axis. this is just far superior than any explanation that would have come from elsewhere. my exam is tomorrow, thank you so fucking much.


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