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Persamaan garis singgung pada lingkaran  yang sejajar garis  adalah ....

Pertanyaan

Persamaan garis singgung pada lingkaran straight L space identical to left parenthesis straight x space – space 3 right parenthesis squared plus left parenthesis straight y space plus space 2 right parenthesis squared equals 16 yang sejajar garis 4 straight х minus 2 straight у minus 7 equals 0 adalah ....

Pembahasan Soal:

Diketahui 

Persamaan garis 4 straight х minus 2 straight у minus 7 equals 0 maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 straight х minus 2 straight у minus 7 end cell equals 0 row cell negative 2 straight y end cell equals cell negative 4 straight x plus 7 end cell row straight y equals cell fraction numerator negative 4 straight x plus 7 over denominator negative 2 end fraction end cell row blank equals cell 2 straight x minus 7 over 2 end cell row straight m equals 2 end table 

Garis sejajar memiliki gradien yang sama, maka gradien garis singgung yang akan kita cari adalah straight m equals 2 

Persamaan garis singgung lingkaran dengan gradien m adalah :

straight y minus straight b equals equals straight m left parenthesis straight x minus straight a right parenthesis plus-or-minus straight r square root of 1 plus straight m squared end root 

Dengan :

lingkaran straight L space identical to left parenthesis straight x space – space 3 right parenthesis squared plus left parenthesis straight y space plus space 2 right parenthesis squared equals 16

Maka :

table attributes columnalign right center left columnspacing 0px end attributes row straight a equals 3 row straight b equals cell negative 2 end cell row straight r equals cell square root of 16 end cell row blank equals 4 end table 

sehingga diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight y minus straight b end cell equals cell equals straight m left parenthesis straight x minus straight a right parenthesis plus-or-minus straight r square root of 1 plus straight m squared end root end cell row cell straight y minus left parenthesis negative 2 right parenthesis end cell equals cell equals 2 left parenthesis straight x minus 3 right parenthesis plus-or-minus 4 square root of 1 plus 2 squared end root end cell row cell straight y plus 2 end cell equals cell equals 2 straight x minus 6 plus-or-minus 4 square root of 1 plus 4 end root end cell row cell straight y plus 2 end cell equals cell 2 straight x minus 6 plus-or-minus 4 square root of 5 end cell row straight y equals cell 2 straight x minus 8 plus-or-minus 4 square root of 5 end cell end table 

Jadii, Persamaan garis singgung pada lingkaran straight L space identical to left parenthesis straight x space – space 3 right parenthesis squared plus left parenthesis straight y space plus space 2 right parenthesis squared equals 16 yang sejajar garis 4 straight х minus 2 straight у minus 7 equals 0 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight y 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x 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 8 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 5 end cell end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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