Sebuah Telaah Elips dan Lingkaran Melalui Sebuah Pendekatan Aljabar Matriks

Rahmat Sagara

Abstract


In this article, ellipse and circle will be learnt in depth via matrix algebra approach. The discussion of the both is started from their classic definition continued by surveying ellipse in matrix form. During the survey, some properties about ellipse will be explained and also, the procedure in drawing the figures can be obtained geometrically using some aspect in geometry: rotation and translation. At the end of the discussion, the new definition of the figures is deduced. Both of them are defined as” a set of points in a plane that are the same distance from a fixed point” but in different point of view about the ‘distance’. The ‘distance’ in the definition is derived from different norm definition. The difference lies on the positive definite matrix used in the norm definition. Base on the new definition, we’ll have the conclusion that circle is a special type of ellipse.

Keywords


circle; distance; ellipse; norm; positive definite matrix

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DOI: https://doi.org/10.18860/ca.v1i2.1709

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CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.