The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS

  • Kim, Dong-Soo (Department of Mathematics, Chonnam National University) ;
  • Seo, Soojeong (Department of Mathematics, Chonnam National University) ;
  • Beom, Woo-In (Department of Mathematics, Chonnam National University) ;
  • Yang, Deukju (Department of Mathematics, Chonnam National University) ;
  • Kang, Juyeon (Department of Mathematics, Chonnam National University) ;
  • Jeong, Jieun (Department of Mathematics, Chonnam National University) ;
  • Song, Booseon (Department of Mathematics, Chonnam National University)
  • Received : 2012.06.01
  • Accepted : 2012.09.03
  • Published : 2012.11.30
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Abstract

Let A and B denote a point, a line or a circle, respectively. For a positive constant $a$, we examine the locus $C_{AB}$($a$) of points P whose distances from A and B are, respectively, in a constant ratio $a$. As a result, we establish some equivalent conditions for conic sections. As a byproduct, we give an easy way to plot points of conic sections exactly by a compass and a straightedge.

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References

  1. Anton, H.: Calculus with analytic geometry, 4th ed.. John Wiley and Sons, Inc., New York, 1992.
  2. Chen, B.-Y., Kim, D.-S. & Kim, Y.H.: New characterizations of W-curves. Publ. Math. Debrecen 69 (2006), 457-472.
  3. Kim, D.-S. & Kang, S.H.: A characterization of conic sections. Honam Math. J. 33 (2011), no. 3, 335-340. https://doi.org/10.5831/HMJ.2011.33.3.335
  4. Kim, D.-S. & Kim, Y.H.: A characterization of ellipses. Amer. Math. Monthly 114/1 (2007), 65-69.
  5. Kim, D.-S., Kim, Y.H. & Park, J.H.: Some properties of tangent lines of parabolas. Kyungpook Math. J., to appear.
  6. Rademacher, H. & Toeplitz, O.: The enjoyment of mathematics. Translated from the second (1933) German edition and with additional chapters by H. Zuckerman. Princeton Science Library, Princeton University Press, Princeton, NJ, 1994.
  7. Simmons, George F.: Calculus with analytic geometry, 2nd ed.. The McGraw-Hill Companies, Inc., New York, 1996.
  8. Yu, Y. & Liu, L.: A characterization of parabola. Bull. Korean Math. Soc. 45 (2008), no. 4, 631-634. https://doi.org/10.4134/BKMS.2008.45.4.631

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