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Persamaan lingkaran yang melalui tiga titik .

Persamaan lingkaran yang melalui tiga titik begin mathsize 14px style A left parenthesis 2 comma negative 4 right parenthesis comma space B left parenthesis 5 comma negative 1 right parenthesis comma space C left parenthesis 2 comma 2 right parenthesis end style.

Jawaban:

Subtitusi ketiga titik ke persamaan lingkaran

begin mathsize 14px style x squared plus y squared plus A x plus B y plus C equals 0 A left parenthesis 2 comma negative 4 right parenthesis rightwards arrow 2 squared plus left parenthesis negative 4 right parenthesis squared plus 2 A minus 4 B plus C equals 0 space space space space space space space space space space space space space space space space space space space space 2 A minus 4 B plus C equals negative 20........ left parenthesis 1 right parenthesis B left parenthesis 5 comma negative 1 right parenthesis rightwards arrow 5 squared plus left parenthesis negative 1 right parenthesis squared plus 5 A minus B plus C equals 0 space space space space space space space space space space space space space space space space space space space space space 5 A minus B plus C equals negative 26......... left parenthesis 2 right parenthesis C left parenthesis 2 comma 2 right parenthesis rightwards arrow 2 squared plus 2 squared plus 2 A plus 2 B plus C equals 0 space space space space space space space space space space space space space space space space space 2 A plus 2 B plus C equals negative 8............ left parenthesis 3 right parenthesis end style

Eliminasi 2A dan C pada persamaan (1) dan (3), diperoleh

begin mathsize 14px style 2 A minus 4 B plus C equals negative 20 bottom enclose 2 A plus 2 B plus C equals negative 8 space space space subscript minus end enclose space space space space space space space space space space space space minus 6 B equals negative 12 space space space space space space space space space space space space space space space space space space B equals 2 end style

Selanjutnya substitusi nilai B ke persamaan (1) dan (2), dan hasilnya eliminasi C

begin mathsize 14px style 2 A plus C equals negative 12 bottom enclose 5 A plus C equals negative 24 subscript minus end enclose 3 A equals negative 12 A equals negative 4 space space space  2 left parenthesis negative 4 right parenthesis plus C equals negative 12 C equals negative 4 end style

Dari nilai A, B dan C yang diperoleh, persamaan lingkarannya adalah

begin mathsize 14px style x squared plus y squared minus 4 x plus 2 y minus 4 equals 0 end style

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