Browsing by Author "Utami, Nurul Andayani"

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    PENGEMBANGAN LEMA HARUKI PADA ELIPS
    (perpustakaan UR, 2021-10) Utami, Nurul Andayani
    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