PENGEMBANGAN LEMA HARUKI PADA ELIPS
No Thumbnail Available
Date
2021-10
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
perpustakaan UR
Abstract
This article discusses the constancy of Haruki's lemma on the ellipse. Given two
nonintersecting chords AB and CD on an ellipse and a variable point P on the
arc AB remote from points C and D, let E and F be the intersections of chords
PC;AB and PD;AB respectively. The value of AE · BF=EF does not depend on
the position of P. The proof is presented by geometric transformations, using the
coordinates of points on the ellipse and using the theorem of the intersection of two
chords on the ellipse. Haruki's lemma is applied to an ellipse centered at O(0; 0)
with an arbitrary chord AB, a horizontal chord AB and a vertical chord AB, so
that the Haruki's lemma constant on the ellipse is as follows:
AE · BF
EF
=
(√
(xe − xa)2 + (ye − ya)2
)
·
(√
(xf − xb)2 + (yf − yb)2
)
√
(xf − xe)2 + (yf − ye)2
Description
Keywords
Geometrical coordinate, intersection of two chords of an ellipse, Haruki's lemma, Haruki's lemma on ellipse