Roboguru

Jika panjang jari-jari lingkaran adalah dua kali panjang jari-jari lingkaran , maka panjang jari-jari lingkaran yang lebih besar adalah....

Jika panjang jari-jari lingkaran x squared plus y squared plus A x plus B y minus 4 equals 0 adalah dua kali panjang jari-jari lingkaran x squared plus y squared plus A x plus B y plus 17 equals 0, maka panjang jari-jari lingkaran yang lebih besar adalah....

  1. square root of 7

  2. 2 square root of 7

  3. 3 square root of 7

  4. 4 square root of 7

  5. 5 square root of 7

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 pertama space dengan space persamaan space straight x squared plus straight y squared plus Ax plus By minus 4 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 straight B close parentheses squared minus open parentheses negative 4 close parentheses end root  box enclose straight r subscript 1 equals square root of 1 fourth straight A squared plus 1 fourth straight B squared plus 4 end root end enclose    Dan space lingkaran space kedua space dengan space persamaan space straight x squared plus straight y squared plus Ax plus By plus 17 equals 0 space  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 straight B close parentheses squared minus 17 end root  box enclose straight r subscript 2 equals square root of 1 fourth straight A squared plus 1 fourth straight B squared minus 17 end root end enclose    straight r subscript 1 equals 2 straight r subscript 2  square root of 1 fourth straight A squared plus 1 fourth straight B squared plus 4 end root equals 2 square root of 1 fourth straight A squared plus 1 fourth straight B squared minus 17 end root  1 fourth straight A squared plus 1 fourth straight B squared plus 4 equals 4 open parentheses 1 fourth straight A squared plus 1 fourth straight B squared minus 17 close parentheses  1 fourth straight A squared plus 1 fourth straight B squared plus 4 equals straight A squared plus straight B squared minus 68  72 equals 3 over 4 straight A squared plus 3 over 4 straight B squared  72 equals 3 over 4 open parentheses straight A squared plus straight B squared close parentheses  straight A squared plus straight B squared equals 72.4 over 3  box enclose straight A squared plus straight B squared equals 96 end enclose    Karena space straight r subscript 1 equals 2 straight r subscript 2 comma space maka space lingkaran space pertama space memiliki space jari minus jari space yang space lebih space  besar comma space dengan  straight r subscript 1 equals square root of 1 fourth straight A squared plus 1 fourth straight B squared plus 4 end root  equals square root of 1 fourth open parentheses straight A squared plus straight B squared close parentheses plus 4 end root  equals square root of 1 fourth open parentheses 96 close parentheses plus 4 end root  equals square root of 24 plus 4 end root  equals square root of 28  equals box enclose 2 square root of 7 end enclose

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