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Tentukan persamaan lingkaran yang memiliki pusat di P left parenthesis negative 3 comma 0 right parenthesis dan menyinggung garis x plus y equals 1 factorial 

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

 persamaan lingkaran yang memiliki pusat di P left parenthesis negative 3 comma 0 right parenthesis dan menyinggung garis x plus y equals 1 adalah x squared plus y squared plus 6 x plus 1 equals 0

Pembahasan

Bentuk umum persamaan garis adalah a x plus b y plus c equals 0.Dengan demikian, pada garis singgung lingkaran x plus y equals 1nilai a equals 1 comma b equals 1 comma space text dan end text space c equals negative 1. 

Jarak titik pusat P left parenthesis negative 3 comma 0 right parenthesis dengan garis singgung yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell open vertical bar fraction numerator a times x subscript 1 plus b times y subscript 1 plus c over denominator square root of a squared plus b squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator left parenthesis 1 right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis 1 right parenthesis left parenthesis 0 right parenthesis plus left parenthesis negative 1 right parenthesis over denominator square root of 1 squared plus 1 squared end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 3 plus 0 minus 1 over denominator square root of 2 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 4 over denominator square root of 2 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 4 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator negative 4 square root of 2 over denominator 2 end fraction close vertical bar end cell row blank equals cell open vertical bar negative 2 square root of 2 close vertical bar end cell row blank equals cell 2 square root of 2 end cell end table 

Sehingga persamaan garis singgung lingkarannya:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis x minus a right parenthesis squared plus left parenthesis y minus b right parenthesis squared end cell equals cell r squared space end cell row cell left parenthesis x minus left parenthesis negative 3 right parenthesis right parenthesis squared plus left parenthesis y minus 0 right parenthesis squared end cell equals cell left parenthesis 2 square root of 2 right parenthesis squared space end cell row cell left parenthesis x plus 3 right parenthesis squared plus y squared end cell equals 8 row cell x squared plus 6 x plus 9 plus y squared minus 8 end cell equals 0 row cell x squared plus y squared plus 6 x plus 1 end cell equals 0 end table 

Dengan demikian, persamaan lingkaran yang memiliki pusat di P left parenthesis negative 3 comma 0 right parenthesis dan menyinggung garis x plus y equals 1 adalah x squared plus y squared plus 6 x plus 1 equals 0

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