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Persamaan garis lurus yang melalui titik potong li...

Persamaan garis lurus yang melalui titik potong lingkaran-lingkaran yang melalui titik (-2,-1) dan menyinggung sumbu-x dan sumbu-y adalah ....

  1. x + 2y + 4 = 0

  2. x + y + 3 = 0

  3. 3x + y + 7 = 0

  4. x + 3y + 5 = 0

  5. 2x + y + 5 = 0

Jawaban:

begin mathsize 14px style Karena space lingkaran space melalui space titik space left parenthesis negative 2 comma negative 1 right parenthesis space serta space menyinggung space  sumbu space straight x space dan space sumbu space straight y comma space maka space lingkaran space akan space berada space di space  kuadran space III. end style

begin mathsize 14px style Maka space pusatnya space straight P left parenthesis negative straight a comma negative straight a right parenthesis space dan space jari minus jarinya space straight r equals straight a  Persamaan space lingkarannya colon  open parentheses straight x plus straight a close parentheses squared plus open parentheses straight y plus straight a close parentheses squared equals straight a squared  Melalui space titik space left parenthesis negative 2 comma negative 1 right parenthesis comma space sehingga colon  open parentheses negative 2 plus straight a close parentheses squared plus open parentheses negative 1 plus straight a close parentheses squared equals straight a squared  4 minus 4 straight a plus straight a squared plus 1 minus 2 straight a plus straight a squared equals straight a squared  straight a squared minus 6 straight a plus 5 equals 0  open parentheses straight a minus 5 close parentheses open parentheses straight a minus 1 close parentheses equals 0  straight a equals 5 space atau space straight a equals 1    Untuk space straight a equals 5 comma space persamaan space lingkarannya colon  open parentheses straight x plus 5 close parentheses squared plus open parentheses straight y plus 5 close parentheses squared equals 5 squared  straight x squared plus 10 straight x plus 25 plus straight y squared plus 10 straight y plus 25 equals 25  straight x squared plus straight y squared plus 10 straight x plus 10 straight y plus 25 equals 0    Untuk space straight a equals 1 comma space persamaan space lingkarannya colon  open parentheses straight x plus 1 close parentheses squared plus open parentheses straight y plus 1 close parentheses squared equals 1 squared  straight x squared plus 2 straight x plus 1 plus straight y squared plus 2 straight y plus 1 equals 1  straight x squared plus straight y squared plus 2 straight x plus 2 straight y plus 1 equals 0    Persamaan space garis space lurus space yang space melalui space titik space potong space kedua space lingkaran colon  straight x squared plus straight y squared plus 10 straight x plus 10 straight y plus 25 equals 0  bottom enclose straight x squared plus straight y squared plus space space 2 straight x plus space space 2 straight y plus space space 1 equals 0 space space minus end enclose  8 straight x plus 8 straight y plus 24 equals 0  straight x plus straight y plus 3 equals 0 end style

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