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January 11th, 2012, 04:52 PM   #1
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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 focus-directrix pairs.

Direction on the directrix would be great cheers no but im pretty clueless on this all round so any help very much appreciated.
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January 11th, 2012, 07:11 PM   #2
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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 non-linear 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 x-axis, and the foci will be at the points

The directices will be the lines

Note: the directrices may also be found with
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January 12th, 2012, 03:11 PM   #3
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Re: Ellipse question (eccentricity e.t.c) - pre exam

Thank you indeed. i will study what your post.
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January 13th, 2012, 09:24 AM   #4
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Re: Ellipse question (eccentricity e.t.c) - pre exam

shockingly bad post by me. forgot to take out the what.
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January 13th, 2012, 09:29 AM   #5
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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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