Jawaban:

Jawaban yang benar adalah E.

Ingat kembali mengenai konsep garis menyinggung lingkaran jika straight D equals 0 dengan straight D equals straight b squared minus 4 ac. Dari soal di atas, dicari persamaan garis yang tidak menyinggung lingkaran x squared plus y squared equals 16. Dengan demikian, dicari nilai straight D less than 0 atau straight D greater than 0.

Garis x equals 4 disubtitusikan ke persamaan x squared plus y squared equals 16, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 16 row cell 4 squared plus y squared end cell equals 16 row cell 16 plus y squared end cell equals 16 row cell y squared end cell equals 0 row straight D equals cell straight b squared minus 4 ac end cell row blank equals cell 0 minus 4 times 1 times 0 end cell row blank equals 0 end table

Garis x equals negative 4 disubtitusikan ke persamaan x squared plus y squared equals 16, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 16 row cell open parentheses negative 4 close parentheses squared plus y squared end cell equals 16 row cell 16 plus y squared end cell equals 16 row cell y squared end cell equals 0 row straight D equals cell straight b squared minus 4 ac end cell row blank equals cell 0 minus 4 times 1 times 0 end cell row blank equals 0 end table

Garis y equals 4 disubtitusikan ke persamaan x squared plus y squared equals 16, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 16 row cell x squared plus 4 squared end cell equals 16 row cell x squared plus 16 end cell equals 16 row cell x squared end cell equals 0 row straight D equals cell straight b squared minus 4 ac end cell row blank equals cell 0 minus 4 times 1 times 0 end cell row blank equals 0 end table

Garis y equals negative 4 disubtitusikan ke persamaan x squared plus y squared equals 16, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 16 row cell x squared plus open parentheses negative 4 close parentheses squared end cell equals 16 row cell x squared plus 16 end cell equals 16 row cell x squared end cell equals 0 row straight D equals cell straight b squared minus 4 ac end cell row blank equals cell 0 minus 4 times 1 times 0 end cell row blank equals 0 end table

Garis x plus y equals 4 diubah menjadi y equals 4 minus x kemusian disubtitusikan ke persamaan x squared plus y squared equals 16, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 16 row cell x squared plus open parentheses 4 minus x close parentheses squared end cell equals 16 row cell x squared plus 16 minus 8 x plus x squared end cell equals 16 row cell 2 x squared minus 8 x end cell equals 0 row straight D equals cell straight b squared minus 4 ac end cell row blank equals cell open parentheses negative 8 close parentheses squared minus 4 times 2 times 0 end cell row blank equals 64 end table

Dari perhitungan di atas diperoleh bahwa garis x plus y equals 4 jika disubtitusikan ke lingkaran x squared plus y squared equals 16 akan menghasilkan nilai straight D greater than 0, sehingga garis tersebut tidak menyinggung lingkaran di 1 titik melainkan memotong lingkaran di 2 titik.

Oleh karena itu, jawaban yang benar adalah E.

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