Foci of an EllipseDate: 06/08/2001 at 13:52:00 From: Scott Nugent Subject: Elliptical foci If the major and minor axis of an ellipse are given, how do I find the focus points? Date: 06/08/2001 at 15:40:43 From: Doctor Floor Subject: Re: Elliptical foci Hi, Scott, Thanks for writing. The foci F1 and F2 of an ellipse lie on its major axis, at equal distances from the center M of the ellipse. Let P be a variable point on the ellipse; then the sum of distances d(P,F1)+d(P,F2) is constant. Now let the major axis meet the ellipse in X1 and X2 and the minor axis in Y1 and Y2. Let a be the length of the major axis. In a figure: Y1 | | X1--F1----M-----F2--X2 | | Y2 Clearly d(X1,F1)+d(X1,F2) = d(X1,F1)+d(X2,F1) = a and thus d(Y1,F1) = d(Y2,F2) = a/2. Knowing this it is not too difficult to find the position of F1 and F2 (for instance we might use Pythagoras' theorem in triangle F1MY1 to compute the distance from M to F1). If you need more help, just write back. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ Date: 06/08/2001 at 15:43:45 From: Doctor Peterson Subject: Re: Elliptical foci Hi, Scott. The foci lie along the major axis, at distance c on either side of the center, where c^2 = a^2 - b^2 You can find this information (and an explanation) by searching our archives for the words "ellipse major minor focus": Analytic Geometry Formulas http://mathforum.org/dr.math/faq/formulas/faq.analygeom_2.html (select Two Dimensions: ellipses) Ellipses: Pythagorean Relationship http://mathforum.org/library/drmath/view/54802.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/08/2001 at 15:51:57 From: Scott Nugent Subject: Re: Elliptical foci Thank you very much! |
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