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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.19 No.4

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SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS

SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.4, pp.315-325
https://doi.org/10.7468/jksmeb.2012.19.4.315
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)
Kim, Dong-Soo, Seo, Soojeong, Beom, Woo-In, Yang, Deukju, Kang, Juyeon, Jeong, Jieun, & Song, Booseon. (2012). SOME EQUIVALENT CONDITIONS FOR CONIC SECTIONS. , 19(4), 315-325, https://doi.org/10.7468/jksmeb.2012.19.4.315

Abstract

Let A and B denote a point, a line or a circle, respectively. For a positive constant <TEX>$a$</TEX>, we examine the locus <TEX>$C_{AB}$</TEX>(<TEX>$a$</TEX>) of points P whose distances from A and B are, respectively, in a constant ratio <TEX>$a$</TEX>. 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.

keywords
parabola, ellipse, hyperbola, conic section, directrix, focus

참고문헌

1.

Calculus with analytic geometry.

2.

New characterizations of W-curves.

3.

(2011). A CHARACTERIZATION OF CONIC SECTIONS. Honam Mathematical Journal, 33(3), 335-340. 10.5831/HMJ.2011.33.3.335.

4.

(2007). A characterization of ellipses. Amer. Math. Monthly, 114/1, 65-69.

5.

(0000). Some properties of tangent lines of parabolas. Kyungpook Math. J., .

6.

The enjoyment of mathematics.

7.

Calculus with analytic geometry.

8.

(2008). A CHARACTERIZATION OF PARABOLA. Bulletin of the Korean Mathematical Society, 45(4), 631-634. 10.4134/BKMS.2008.45.4.631.

한국수학교육학회지시리즈B:순수및응용수학

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