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6. Sebuah lingkaran melalui titik begin mathsize 14px style straight A left parenthesis negative 1 comma 2 right parenthesis comma space straight B left parenthesis 7 comma negative 2 right parenthesis comma end style dan begin mathsize 14px style straight C left parenthesis 8 comma 5 right parenthesis. end style Persamaan lingkaran itu adalah...undefined       space space                      undefined   space   space undefined  

  1. begin mathsize 14px style x squared plus y squared minus 8 x minus 4 y minus 5 equals 0 end style 

  2. begin mathsize 14px style x squared plus y squared plus 8 x minus 4 y minus 5 equals 0 end style 

  3. begin mathsize 14px style x squared plus y squared plus 8 x plus 4 y plus 5 equals 0 end style 

  4. begin mathsize 14px style x squared plus y squared minus 8 x minus 4 y plus 5 equals 0 end style 

  5. begin mathsize 14px style x squared plus y squared minus 8 x plus 4 y minus 5 equals 0 end style 

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A. space  

Pembahasan

Perhatikan penghitungan berikut!
 

 begin mathsize 14px style Persamaan space lingkaran open parentheses x minus a close parentheses squared plus open parentheses y minus b close parentheses squared equals r squared  Titik space straight A left parenthesis negative 1 comma 2 right parenthesis open parentheses negative 1 minus a close parentheses squared plus open parentheses 2 minus b close parentheses squared equals r squared a squared plus b squared plus 2 a minus 4 b plus 1 plus 4 equals r squared a squared plus b squared plus 2 a minus 4 b plus 5 equals r squared.... left parenthesis straight i right parenthesis  Titik space straight B left parenthesis 7 comma negative 2 right parenthesis open parentheses 7 minus a close parentheses squared plus open parentheses negative 2 minus b close parentheses squared equals r to the power of italic 2 a squared plus b squared minus 14 a plus 4 b plus 49 plus 4 equals r to the power of italic 2 a squared plus b squared minus 14 a plus 4 b plus 53 equals r to the power of italic 2.... left parenthesis ii right parenthesis  Titik space straight C left parenthesis 8 comma 5 right parenthesis open parentheses 8 minus a close parentheses squared plus open parentheses 5 minus b close parentheses squared equals r to the power of italic 2 a to the power of italic 2 plus b to the power of italic 2 minus 16 a minus 10 b plus 64 plus 25 equals r to the power of italic 2 a to the power of italic 2 plus b to the power of italic 2 minus 16 a minus 10 b plus 89 italic equals r to the power of italic 2 italic. italic. italic. italic. left parenthesis iii right parenthesis  Eliminasi space pers. left parenthesis straight i right parenthesis space dan space left parenthesis ii right parenthesis bottom enclose a squared plus b squared plus 2 a minus 4 b plus 5 equals r squared a squared plus b squared minus 14 a plus 4 b plus 53 equals r squared space space space space space space minus end enclose 16 a minus 8 b minus 48 equals 0.... left parenthesis iv right parenthesis  Eliminasi space pers. left parenthesis ii right parenthesis space dan space left parenthesis iii right parenthesis bottom enclose a to the power of italic 2 plus b to the power of italic 2 minus 14 a plus 4 b plus 53 equals r to the power of italic 2 a to the power of italic 2 plus b squared minus 16 a minus 10 b plus 89 equals r to the power of italic 2 italic space italic space italic space italic space space space minus end enclose 2 a plus 14 b minus 36 equals 0.... left parenthesis straight v right parenthesis  Eliminasi space pers. left parenthesis iv right parenthesis space dan space left parenthesis straight v right parenthesis bottom enclose table row cell 16 a minus 8 b minus 48 equals 0 end cell row cell 2 a plus 14 b minus 36 equals 0 end cell end table space table row cell open vertical bar table row cell cross times 1 end cell row cell cross times 8 end cell end table close vertical bar end cell end table table row cell 16 a minus 8 b minus 48 equals 0 end cell row cell 16 a plus 112 b minus 288 equals 0 space end cell end table end enclose space minus space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 120 b plus 240 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 120 b equals negative 240 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space b equals 2  substitusi space nilai space b space ke space pers. space left parenthesis straight v right parenthesis 2 a plus 14 b minus 36 equals 0 2 a plus 14 open parentheses 2 close parentheses minus 36 equals 0 2 a plus 28 minus 36 equals 0 2 a equals 8 a equals 4  substistusi space nilai space a space dan space b space ke space pers. left parenthesis straight i right parenthesis a squared plus b squared plus 2 a minus 4 b plus 5 equals r squared 4 squared plus 2 squared plus 2 open parentheses 4 close parentheses minus 4 open parentheses 2 close parentheses plus 5 equals r squared 25 equals r squared plus-or-minus square root of 25 equals r plus-or-minus 5 equals r pilih space r equals 5 space karena space jari minus jari space memiliki space nilai space positif  substitusi space nilai space a comma space b comma space dan space r space ke space pers. lingkaran open parentheses x minus a close parentheses squared plus open parentheses y minus b close parentheses squared equals r squared open parentheses x minus 4 close parentheses squared plus open parentheses y minus 2 close parentheses squared equals 5 squared x squared plus y squared minus 8 x minus 4 y plus 16 plus 4 equals 25 x squared plus y squared minus 8 x minus 4 y plus 20 equals 25 x squared plus y squared minus 8 x minus 4 y plus 20 minus 25 equals 0 x squared plus y squared minus 8 x minus 4 y minus 5 equals 0   end style 

Oleh karena itu, jawaban yang benar adalah A. space  

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