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Tentukan persamaan garis singgung grafik  yang sejajar garis .

Pertanyaan

Tentukan persamaan garis singgung grafik y equals x squared minus 4 x minus 5 yang sejajar garis y equals 2 x minus 5.

Pembahasan Soal:

Diketahui :
kurva = y equals f left parenthesis x right parenthesis equals x squared minus 4 x minus 5 maka y to the power of apostrophe equals f to the power of apostrophe left parenthesis x right parenthesis equals 2 x minus 4
Misalkan :
m= gradien garis singgung kurva
m2 = gradien garis 2 x minus y minus 5 equals 0 straight a equals 2 comma space straight b equals negative 1 comma space straight c equals negative 5 

maka straight m subscript 2 equals fraction numerator negative straight a over denominator straight b end fraction equals fraction numerator negative 2 over denominator negative 1 end fraction equals 2

Karena garis singgung kurva sejajar dengan garis 2 x minus y minus 5 equals 0 berlaku m1 =m2 = 2.

Sedangkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m subscript 1 end cell equals cell f to the power of apostrophe left parenthesis x right parenthesis end cell row blank rightwards double arrow cell 2 equals 2 x subscript 1 minus 4 end cell row blank rightwards double arrow cell 6 equals 2 x subscript 1 end cell row blank rightwards double arrow cell 3 equals x subscript 1 end cell end table

Diperoleh,

table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript 1 end cell equals cell f left parenthesis x subscript 1 right parenthesis end cell row blank equals cell f left parenthesis 3 right parenthesis equals 3 squared minus 4 left parenthesis 3 right parenthesis minus 5 end cell row blank equals cell 9 minus 12 minus 5 end cell row blank equals cell negative 8 end cell end table

PGS kurva yang dicari :

table attributes columnalign right center left columnspacing 0px end attributes row cell y minus y subscript 1 end cell equals cell straight m subscript 1 left parenthesis x minus x subscript 1 right parenthesis end cell row cell y minus left parenthesis negative 8 right parenthesis end cell equals cell 2 left parenthesis x minus 3 right parenthesis end cell row cell y plus 8 end cell equals cell 2 x minus 6 end cell row y equals cell 2 x minus 14 space atau space 2 x minus y minus 14 equals 0 end cell end table

Jadi, persamaan garis singgungnya adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 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 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 14 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank atau end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space 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 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 y 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 14 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 0 end table.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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