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Pertanyaan

Jika panjang jari-jari lingkaran x squared plus y squared plus A x plus B y minus 10 equals 0 adalah dua kali panjang jari-jari lingkaran x squared plus y squared plus A x plus B y plus 20 equals 0, panjang jari-jari lingkaran yang lebih besar adalah...

  1. square root of 10

  2. 2 square root of 10

  3. 3 square root of 10

  4. 4 square root of 10

  5. 5 square root of 10

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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 10 equals 0  memiliki space jari minus jari space  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 10 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 10 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 20 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 straight B close parentheses squared minus 20 end root  box enclose straight r subscript 2 equals square root of 1 fourth straight A squared plus 1 fourth straight B squared minus 20 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 10 end root equals 2 square root of 1 fourth straight A squared plus 1 fourth straight B squared minus 20 end root  1 fourth straight A squared plus 1 fourth 4 straight B squared plus 10 equals 4 open parentheses 1 fourth straight A squared plus 1 fourth straight B squared minus 20 close parentheses  1 fourth straight A squared plus 1 fourth straight B squared plus 10 equals straight A squared plus straight B squared minus 80  90 equals 3 over 4 straight A squared plus 3 over 4 straight B squared  90 equals 3 over 4 left parenthesis straight A squared plus straight B squared right parenthesis  straight A squared plus straight B squared equals 90.4 over 3  box enclose straight A squared plus straight B squared equals 120 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 10 end root  equals square root of 1 fourth open parentheses straight A squared plus straight B squared close parentheses plus 10 end root  equals square root of 1 fourth open parentheses 120 close parentheses plus 10 end root  equals square root of 30 plus 10 end root  equals square root of 40  equals box enclose 2 square root of 10 end enclose

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