Use the following ellipse : (F, F' are foci of the ellipse and the line passes through it.) Prove : I tried to prove it using directrix, but it got way too complicated.
Last edited by lanierms; September 8th 2012 at 06:33 AM.
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Originally Posted by lanierms Use the following ellipse : (F, F' are foci of the ellipse and the line passes through it.) Prove : I tried to prove it using directrix, but it got way too complicated. If the equality is true for all points P & Q on ellipse then letting P(a,0) & Q(-a,0) we will have: In the general case when P & Q are elsewhere on the ellipse. We have: Move x-y coordinate's origin to focus F...then PF & QF will be:
Last edited by MaxJasper; September 8th 2012 at 08:34 PM.
It seems like a nice proof, but can there be another way without using eccentricity?
Variation of by fpr a=3, b=2
Last edited by MaxJasper; September 9th 2012 at 04:30 PM.
I don't quite understand the part where you said PF = a(1-ecos(theta)) Can you please explain more about it?
OF = e*a
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