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Jika lingkaran  mempunyai panjang jari jari a, mak...

Jika lingkaran x squared plus y squared minus a x minus a y minus a equals 0 mempunyai panjang jari jari a, maka nilai a 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 space 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 dengan space persamaan space straight x squared plus straight y squared minus ax minus ay minus straight a equals 0 space memiliki  jari minus jari  straight r equals square root of open parentheses negative 1 half open parentheses negative straight a close parentheses close parentheses squared plus open parentheses negative 1 half open parentheses negative straight a close parentheses close parentheses squared minus open parentheses negative straight a close parentheses end root equals square root of 1 fourth straight a squared plus 1 fourth straight a squared plus straight a end root equals box enclose square root of 1 half straight a squared plus straight a end root end enclose    Berdasarkan space soal space didapat space jari minus jari space lingkaran space box enclose straight r equals straight a end enclose  Maka  square root of 1 half straight a squared plus straight a end root equals straight a  Kuadratkan comma space sehingga space didapat  1 half straight a squared plus straight a equals straight a squared  1 half straight a squared minus straight a equals 0  straight a open parentheses 1 half straight a minus 1 close parentheses equals 0  Maka  box enclose straight a equals 0 end enclose  atau  1 half straight a minus 1 equals 0 rightwards arrow 1 half straight a equals 1 rightwards arrow box enclose straight a equals 2 end enclose

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