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Diketahui persamaan lingkaran sebagai berikut. Salah satu persamaan garis singgung persekutuan dua lingkaran di atas adalah ….

Pertanyaan

Diketahui persamaan lingkaran sebagai berikut.

begin mathsize 14px style straight L subscript 1 blank colon open parentheses x plus 4 close parentheses squared plus open parentheses y minus 4 close parentheses squared equals 1 straight L subscript 2 blank colon open parentheses x plus 7 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 end style

Salah satu persamaan garis singgung persekutuan dua lingkaran di atas adalah ….

  1. begin mathsize 14px style 4 y equals 3 x plus 11 end style

  2. begin mathsize 14px style 4 y equals 3 x plus 33 end style

  3. begin mathsize 14px style 3 y equals 4 x plus 33 end style

  4. begin mathsize 14px style 4 y equals 3 x plus 9 end style

  5. begin mathsize 14px style 3 y equals 3 x plus 2 end style

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Terlebih dahulu tentukan pusat dan jari-jari masing-masing lingkaran.

Untuk begin mathsize 14px style straight L subscript 1 blank colon open parentheses x plus 4 close parentheses squared plus open parentheses y minus 4 close parentheses squared equals 1 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 1 end cell equals cell left parenthesis negative 4 , space 4 right parenthesis end cell row cell r subscript 1 end cell equals 1 end table end style

Untuk begin mathsize 14px style straight L subscript 2 blank colon open parentheses x plus 7 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 2 squared end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 2 end cell equals cell left parenthesis negative 7 comma space 5 right parenthesis end cell row cell r subscript 2 end cell equals 2 end table end style

Kemudian, perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P subscript 1 straight P subscript 2 end cell equals cell square root of left parenthesis negative 7 plus 4 right parenthesis squared plus left parenthesis 5 minus 4 right parenthesis squared end root end cell row blank equals cell square root of 9 plus 1 end root end cell row blank equals cell square root of 10 end cell end table end style

dan

begin mathsize 14px style r subscript 1 plus r subscript 2 equals 1 plus 2 equals 3 end style

Karena begin mathsize 14px style straight P subscript 1 straight P subscript 2 greater than r subscript 1 plus r subscript 2 end style, maka dapat disimpulkan bahwa begin mathsize 14px style straight L subscript 1 end style dan begin mathsize 14px style straight L subscript 2 end style saling lepas di luar. Oleh karena itu, akan terdapat 3 atau 4 persamaan garis singgung persekutuan kedua lingkaran tersebut.

Perhatikan bahwa jarak titik pusat ke garis singgung akan sama dengan jari-jari dari masing-masing lingkaran.

Jarak titik begin mathsize 14px style straight P subscript 1 end style yaitu begin mathsize 14px style open parentheses negative 4 comma space 4 close parentheses end style ke garis singgung begin mathsize 14px style y minus m x minus c equals 0 end style adalah sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 1 open parentheses 4 close parentheses minus m open parentheses negative 4 close parentheses minus c over denominator square root of open parentheses negative m close parentheses squared plus 1 squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell 4 plus 4 m minus c end cell equals cell plus-or-minus square root of 1 plus m squared end root end cell row cell negative c end cell equals cell plus-or-minus square root of 1 plus m squared end root minus 4 minus 4 m blank horizontal ellipsis space left parenthesis 1 right parenthesis end cell end table end style

Selanjutnya, jarak titik begin mathsize 14px style straight P subscript 2 end style yaitu begin mathsize 14px style open parentheses negative 7 comma space 5 close parentheses end style ke garis singgung begin mathsize 14px style y minus m x minus c equals 0 end style adalah sebagai berikut. 

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 1 open parentheses 5 close parentheses minus m open parentheses negative 7 close parentheses minus c over denominator square root of open parentheses negative m close parentheses squared plus 1 squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell 5 plus 7 m minus c end cell equals cell plus-or-minus 2 square root of 1 plus m squared end root end cell row cell negative c end cell equals cell plus-or-minus 2 square root of 1 plus m squared end root minus 5 minus 7 m space horizontal ellipsis space left parenthesis 2 right parenthesis end cell end table end style

Kemudian, substitusi persamaan (1) ke persamaan (2) di atas.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 1 plus m squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 1 plus m squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank m end table end style 

Dari bentuk di atas, terdapat 4 kemungkinan, yaitu sebagai berikut.

Kemungkinan 1.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 1 plus m squared end root minus 4 minus 4 m end cell equals cell 2 square root of 1 plus m squared end root minus 5 minus 7 m end cell row cell square root of 1 plus m squared end root minus 2 square root of 1 plus m squared end root end cell equals cell 4 plus 4 m minus 5 minus 7 m end cell row cell negative square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell end table end style

Kemungkinan 2.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 1 plus m squared end root minus 4 minus 4 m end cell equals cell negative 2 square root of 1 plus m squared end root minus 5 minus 7 m end cell row cell square root of 1 plus m squared end root plus 2 square root of 1 plus m squared end root end cell equals cell 4 plus 4 m minus 5 minus 7 m end cell row cell 3 square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell end table end style

Kemungkinan 3.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative square root of 1 plus m squared end root minus 4 minus 4 m end cell equals cell 2 square root of 1 plus m squared end root minus 5 minus 7 m end cell row cell negative square root of 1 plus m squared end root minus 2 square root of 1 plus m squared end root end cell equals cell 4 plus 4 m minus 5 minus 7 m end cell row cell negative 3 square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell end table end style

Kemungkinan 4.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative square root of 1 plus m squared end root minus 4 minus 4 m end cell equals cell negative 2 square root of 1 plus m squared end root minus 5 minus 7 m end cell row cell negative square root of 1 plus m squared end root plus 2 square root of 1 plus m squared end root end cell equals cell 4 plus 4 m minus 5 minus 7 m end cell row cell square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell end table end style

Dari 4 kemungkinan di atas, dapat disederhanakn menjadi 2, yaitu sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell plus-or-minus 3 square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell row cell plus-or-minus square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell end table end style

Kemungkinan 1.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell plus-or-minus 3 square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell row cell open parentheses plus-or-minus 3 square root of 1 plus m squared end root close parentheses squared end cell equals cell left parenthesis negative 3 m minus 1 right parenthesis squared end cell row cell 9 open parentheses 1 plus m squared close parentheses end cell equals cell 9 m squared plus 6 m plus 1 end cell row cell 9 plus 9 m squared end cell equals cell 9 m squared plus 6 m plus 1 end cell row 9 equals cell 6 m plus 1 end cell row 8 equals cell 6 m end cell row cell 4 over 3 end cell equals m end table end style

Kemungkinan 2.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell plus-or-minus square root of 1 plus m squared end root end cell equals cell negative 3 m minus 1 end cell row cell open parentheses plus-or-minus square root of 1 plus m squared end root close parentheses squared end cell equals cell left parenthesis negative 3 m minus 1 right parenthesis squared end cell row cell 1 plus m squared end cell equals cell 9 m squared plus 6 straight m plus 1 end cell row cell 8 m squared plus 6 m end cell equals 0 row cell 2 m left parenthesis 4 m plus 3 right parenthesis end cell equals 0 row m equals cell 0 blank atau blank m equals negative 3 over 4 end cell end table end style

Untuk begin mathsize 14px style m equals 4 over 3 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell plus-or-minus square root of 1 plus open parentheses 4 over 3 close parentheses squared end root minus 4 minus 4 open parentheses 4 over 3 close parentheses end cell row blank equals cell plus-or-minus square root of 1 plus 16 over 9 end root minus 4 minus 16 over 3 end cell row blank equals cell plus-or-minus square root of 25 over 9 end root minus 28 over 3 end cell row blank equals cell plus-or-minus 5 over 3 minus 28 over 3 end cell end table end style

Dari bentuk di atas didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell 5 over 3 minus 28 over 3 end cell row cell negative c end cell equals cell negative 23 over 3 end cell row c equals cell 23 over 3 end cell end table end style

atau

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell negative 5 over 3 minus 28 over 3 end cell row cell negative c end cell equals cell negative 11 end cell row c equals 11 end table end style

Untuk begin mathsize 14px style m equals 0 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell plus-or-minus square root of 1 plus 0 squared end root minus 4 minus 4 open parentheses 0 close parentheses end cell row blank equals cell plus-or-minus square root of 1 minus 4 minus 0 end cell row blank equals cell plus-or-minus 1 minus 4 end cell end table end style

Dari bentuk di atas didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell 1 minus 4 end cell row cell negative c end cell equals cell negative 3 end cell row c equals 3 end table end style

atau

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell negative 1 minus 4 end cell row cell negative c end cell equals cell negative 5 end cell row c equals 5 end table end style

Untuk begin mathsize 14px style m equals negative 3 over 4 end style, didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell plus-or-minus square root of 1 plus open parentheses negative 3 over 4 close parentheses squared end root minus 4 minus 4 open parentheses negative 3 over 4 close parentheses end cell row blank equals cell plus-or-minus square root of 1 plus 9 over 16 end root minus 4 plus 3 end cell row blank equals cell plus-or-minus square root of 25 over 16 end root minus 1 end cell row blank equals cell plus-or-minus 5 over 4 minus 1 end cell end table end style

Dari bentuk di atas didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell 5 over 4 minus 1 end cell row cell negative c end cell equals cell 1 fourth end cell row c equals cell negative 1 fourth end cell end table end style

atau

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative c end cell equals cell negative 5 over 4 minus 1 end cell row cell negative c end cell equals cell negative 9 over 4 end cell row c equals cell 9 over 4 end cell end table end style

Jadi kita peroleh 6 pasangan undefined dan undefined, yaitu sebagai berikut.

  1. begin mathsize 14px style m equals 4 over 3 end style dan undefined
  2. begin mathsize 14px style m equals 4 over 3 end style dan undefined
  3. undefined dan undefined
  4. undefined dan undefined
  5. begin mathsize 14px style m equals negative 3 over 4 end style dan undefined
  6. begin mathsize 14px style m equals negative 3 over 4 end style dan begin mathsize 14px style c equals 9 over 4 end style

Cek untuk nilai begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 23 over 3 end style apakah memenuhi atau tidak.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses 4 over 3 close parentheses minus begin display style 23 over 3 end style over denominator square root of 1 plus open parentheses 4 over 3 close parentheses squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 5 over denominator begin display style 5 over 3 end style end fraction close vertical bar end cell equals 1 row cell vertical line 3 vertical line end cell equals cell 1 blank left parenthesis bold SALAH right parenthesis end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses 4 over 3 close parentheses minus begin display style 23 over 3 end style over denominator square root of 1 plus open parentheses 4 over 3 close parentheses squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator begin display style 20 over 3 end style over denominator begin display style 5 over 3 end style end fraction close vertical bar end cell equals 2 row cell vertical line 4 vertical line end cell equals cell 2 blank left parenthesis bold SALAH right parenthesis end cell end table end style

Karena keduanya salah, maka pasangan nilai begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 23 over 3 end style TIDAK MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Cek untuk nilai begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 11 end style apakah memenuhi atau tidak.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses 4 over 3 close parentheses minus 11 over denominator square root of 1 plus open parentheses 4 over 3 close parentheses squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar negative 1 close vertical bar end cell equals cell 1 blank open parentheses bold BENAR close parentheses end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses 4 over 3 close parentheses minus 11 over denominator square root of 1 plus open parentheses 4 over 3 close parentheses squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar 2 close vertical bar end cell equals cell 2 blank open parentheses bold BENAR close parentheses end cell row blank blank blank row blank blank blank end table end style 

Karena keduanya benar, maka pasangan nilai begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 11 end style MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Cek untuk nilai undefined dan begin mathsize 14px style c equals 3 end style apakah memenuhi atau tidak.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses 0 close parentheses minus 3 over denominator square root of 1 plus 0 squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar 1 close vertical bar end cell equals cell 1 blank open parentheses bold BENAR close parentheses end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses 0 close parentheses minus 3 over denominator square root of 1 plus 0 squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar 2 close vertical bar end cell equals cell 2 blank open parentheses bold BENAR close parentheses end cell row blank blank blank end table end style

Karena keduanya benar, maka pasangan nilai undefined dan begin mathsize 14px style c equals 3 end style MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Cek untuk nilai undefined dan begin mathsize 14px style c equals 5 end style apakah memenuhi atau tidak.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses 0 close parentheses minus 5 over denominator square root of 1 plus 0 squared end root end fraction close vertical bar end cell equals 1 row cell vertical line minus 1 vertical line end cell equals cell 1 blank left parenthesis bold BENAR right parenthesis end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses 0 close parentheses minus 5 over denominator square root of 1 plus 0 squared end root end fraction close vertical bar end cell equals 2 row cell vertical line 0 vertical line end cell equals cell 2 blank left parenthesis bold SALAH right parenthesis end cell end table end style

Karena hanya salah satu saja yang bernilai benar, maka pasangan nilai undefined dan begin mathsize 14px style c equals 5 end style TIDAK MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Cek untuk nilai begin mathsize 14px style m equals negative 3 over 4 end style  dan begin mathsize 14px style c equals negative 1 fourth end style apakah memenuhi atau tidak.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses negative 3 over 4 close parentheses plus 1 fourth over denominator square root of 1 plus open parentheses negative 3 over 4 close parentheses squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar vertical line fraction numerator 5 over 4 over denominator begin display style 5 over 4 end style end fraction vertical line close vertical bar end cell equals 1 row cell vertical line 1 vertical line end cell equals cell 1 blank left parenthesis bold BENAR right parenthesis end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses negative 3 over 4 close parentheses plus 1 fourth over denominator square root of 1 plus open parentheses negative 3 over 4 close parentheses squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar 0 close vertical bar end cell equals cell 2 blank left parenthesis bold SALAH right parenthesis end cell end table end style

Karena hanya salah satu saja yang bernilai benar, maka pasangan nilai begin mathsize 14px style m equals negative 3 over 4 end style dan begin mathsize 14px style c equals negative 1 fourth end style TIDAK MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Cek untuk nilai begin mathsize 14px style m equals negative 3 over 4 end style  dan begin mathsize 14px style c equals 9 over 4 end style apakah memenuhi atau tidak. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar fraction numerator 4 plus 4 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar fraction numerator 4 plus 4 open parentheses negative 3 over 4 close parentheses minus 9 over 4 over denominator square root of 1 plus open parentheses negative 3 over 4 close parentheses squared end root end fraction close vertical bar end cell equals 1 row cell open vertical bar negative 1 close vertical bar end cell equals cell 1 blank open parentheses bold BENAR close parentheses end cell row blank blank blank row cell open vertical bar fraction numerator 5 plus 7 m minus c over denominator square root of 1 plus m squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar fraction numerator 5 plus 7 open parentheses negative 3 over 4 close parentheses minus 9 over 4 over denominator square root of 1 plus open parentheses negative 3 over 4 close parentheses squared end root end fraction close vertical bar end cell equals 2 row cell open vertical bar negative 2 close vertical bar end cell equals cell 2 blank open parentheses bold BENAR close parentheses end cell row blank blank blank end table end style

Karena keduanya benar, maka pasangan nilai begin mathsize 14px style m equals negative 3 over 4 end style  dan begin mathsize 14px style c equals 9 over 4 end style MEMENUHI persamaan garis singgung persekutuan yang diinginkan.

Jadi diperoleh 3 pasangan nilai begin mathsize 14px style m end style dan begin mathsize 14px style c end style yang memenuhi, yaitu sebagai berikut.

  1. begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 11 end style
  2. undefined dan begin mathsize 14px style c equals 3 end style
  3. begin mathsize 14px style m equals negative 3 over 4 end style  dan begin mathsize 14px style c equals 9 over 4 end style

Untuk begin mathsize 14px style m equals 4 over 3 end style dan begin mathsize 14px style c equals 11 end style, didapat persamaan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell m x plus c end cell row y equals cell 4 over 3 x plus 11 end cell row cell 3 y end cell equals cell 4 x plus 33 end cell row blank blank blank row blank blank blank end table end style

Untuk undefined dan begin mathsize 14px style c equals 3 end style, didapat persamaan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell m x plus c end cell row y equals 3 row blank blank blank end table end style

Untuk begin mathsize 14px style m equals negative 3 over 4 end style  dan begin mathsize 14px style c equals 9 over 4 end style, didapat persamaan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell m x plus c end cell row y equals cell negative 3 over 4 x plus 9 over 4 end cell row cell 4 y end cell equals cell negative 3 x plus 9 end cell end table end style

Perhatikan gambar berikut!

Dengan demikian, persamaan garis singgung persekutuan kedua lingkaran tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell 3 y equals 4 x plus 33 end cell cell... space open parentheses 1 close parentheses end cell row cell y equals 3 end cell cell... space open parentheses 2 close parentheses end cell row cell 4 y equals negative 3 x plus 9 end cell cell... space open parentheses 3 close parentheses end cell end table end cell end table end style

Berdasarkan pilihan jawaban di atas, salah satu persamaan garis singgung persekutuan dua lingkaran tersebut adalah begin mathsize 14px style 3 y equals 4 x plus 33 end style.

Jadi, jawaban yang tepat adalah C.

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