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Jika panjang jari-jari lingkaran dan berturut-turut adalah 2 dan , maka nilai C adalah....

Jika panjang jari-jari lingkaran x squared plus y squared plus A x plus 2 A y plus C equals 0 dan x squared plus y squared plus A x plus 3 A y plus C equals 0 berturut-turut adalah 2 dan square root of 10, maka nilai C adalah....

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Jawaban:

Lingkaran space dengan space persamaan space straight x squared plus straight y squared plus Ax plus By plus straight C equals 0 space memiliki  jari minus jari  straight r equals square root of open parentheses negative 1 half straight A close parentheses squared plus open parentheses negative 1 half straight B close parentheses squared minus straight C end root    Sehingga space lingkaran space pertama space dengan space persamaan space straight x squared plus straight y squared plus Ax plus 2 Ay plus straight C equals 0  memiliki space jari minus jari  straight r subscript 1 equals square root of open parentheses negative 1 half straight A close parentheses squared plus open parentheses negative 1 half open parentheses 2 straight A close parentheses close parentheses squared minus straight C end root  2 equals square root of 1 fourth straight A squared plus straight A squared minus straight C end root  2 equals square root of 5 over 4 straight A squared minus straight C end root  box enclose 4 equals 5 over 4 straight A squared minus straight C end enclose    Dan space lingkaran space kedua space dengan space persamaan space straight x squared plus straight y squared plus Ax plus 3 Ay plus straight C equals 0  memiliki space jari minus jari  straight r subscript 2 equals square root of open parentheses negative 1 half straight A close parentheses squared plus open parentheses negative 1 half open parentheses 3 straight A close parentheses close parentheses squared minus straight C end root  square root of 10 equals square root of 1 fourth straight A squared plus 9 over 4 straight A squared minus straight C end root  square root of 10 equals square root of 10 over 4 straight A squared minus straight C end root  box enclose 10 equals 10 over 4 straight A squared minus straight C end enclose    Perhatikan space kedua space persamaan  4 equals 5 over 4 straight A squared minus straight C  bottom enclose 10 equals 10 over 4 straight A squared minus straight C minus end enclose  minus 6 equals negative 5 over 4 straight A squared  box enclose straight A squared equals 24 over 5 end enclose  Sehingga space box enclose straight C equals 2 end enclose.

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