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Jika lingkaran  dan  berturut-turut berjari-jari 5...

Jika lingkaran x squared plus y squared plus 2 A x plus B y equals 0 dan x squared plus y squared plus A x plus 2 B y equals 0 berturut-turut berjari-jari 5 dan 10, maka jari-jari lingkaran x squared plus y squared plus A x plus B y equals 0 spaceadalah ...

  1. square root of 5

  2. square root of 10

  3. 5

  4. 10

  5. 15

Jawaban:

Ingat space factorial  straight x squared plus straight y squared plus Ax plus By plus straight C equals 0 space memiliki  Pusat space equals space open parentheses negative 1 half straight A comma negative 1 half straight B close parentheses  Jari minus jari space equals space square root of 1 fourth straight A squared plus 1 fourth straight B squared minus straight C end root    straight x squared plus straight y squared plus 2 Ax plus By equals 0  straight r equals square root of 1 fourth left parenthesis 2 straight A right parenthesis squared plus 1 fourth open parentheses straight B close parentheses squared end root  5 equals square root of straight A squared plus 1 fourth straight B squared end root  box enclose straight A squared plus 1 fourth straight B squared equals 25 end enclose space... space left parenthesis 1 right parenthesis    straight x squared plus straight y squared plus Ax plus 2 By equals 0  straight r equals square root of 1 fourth straight A squared plus 1 fourth open parentheses 2 straight B close parentheses squared end root  10 equals square root of 1 fourth straight A squared plus straight B squared end root  box enclose 1 fourth straight A squared plus straight B squared equals 100 end enclose space... left parenthesis 2 right parenthesis    Eliminasi space persamaan space left parenthesis 1 right parenthesis space dan space left parenthesis 2 right parenthesis  bottom enclose table row cell straight A squared plus 1 fourth straight B squared equals 25 end cell row cell 1 fourth straight A squared plus straight B squared equals 100 end cell end table open parentheses table row cell cross times 1 end cell row cell cross times 1 fourth end cell end table close parentheses end enclose  table row cell straight A squared plus 1 fourth straight B squared equals 25 end cell row cell bottom enclose 1 over 16 straight A squared plus 1 fourth straight B squared equals 25 space minus end enclose end cell end table  15 over 16 straight A squared equals 0 rightwards double arrow box enclose straight A equals 0 end enclose  0 squared plus 1 fourth straight B squared equals 25  box enclose straight B squared equals 100 end enclose    Maka space persamaan space lingkaran space straight x squared plus straight y squared plus Ax plus By equals 0  straight r equals square root of 1 fourth straight A squared plus 1 fourth straight B squared end root  straight r equals square root of 1 fourth left parenthesis 0 right parenthesis squared plus 1 fourth open parentheses 100 close parentheses end root  box enclose straight r equals 5 end enclose

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