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Diberikan  dan . Persamaan garis singgung pada lingkaran  yang tegak lurus garis PQ adalah ....

Pertanyaan

Diberikan straight P left parenthesis negative 2 comma space 3 right parenthesis dan straight Q left parenthesis 4 comma space 5 right parenthesis. Persamaan garis singgung pada lingkaran straight L identical to straight x squared plus straight y squared minus 4 straight x plus 6 straight y equals 68 yang tegak lurus garis PQ adalah ....

Pembahasan Soal:

Gradien garis yang melalui 2 titik straight P left parenthesis negative 2 comma space 3 right parenthesis dan straight Q left parenthesis 4 comma space 5 right parenthesis adalah :

table attributes columnalign right center left columnspacing 0px end attributes row straight m equals cell fraction numerator straight Y subscript 2 minus straight Y subscript 1 over denominator straight X subscript 2 minus straight X subscript 1 end fraction end cell row blank equals cell fraction numerator 5 minus 3 over denominator 4 minus left parenthesis negative 2 right parenthesis end fraction end cell row blank equals cell 2 over 6 end cell row blank equals cell 1 third end cell end table 

gradien garis saling tegak lurus berlaku m subscript 1 cross times m subscript 2 equals negative 1 maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m subscript 1 cross times straight m subscript 2 end cell equals cell negative 1 end cell row cell 1 third cross times straight m subscript 2 end cell equals cell negative 1 end cell row cell straight m subscript 2 end cell equals cell negative 3 end cell end table 

Gradien garis singgung lingkaran yang mau kita tentukan adalah straight m subscript 2 equals negative 3.

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 

Persamaan lingkaran : straight L identical to straight x squared plus straight y squared minus 4 straight x plus 6 straight y equals 68

table attributes columnalign right center left columnspacing 0px end attributes row straight a equals cell negative 1 half times left parenthesis negative 4 right parenthesis end cell row blank equals 2 row straight b equals cell negative 1 half times left parenthesis 6 right parenthesis end cell row blank equals cell negative 3 end cell row straight r equals cell square root of 2 squared plus left parenthesis negative 3 right parenthesis squared plus 68 end root end cell row blank equals cell square root of 4 plus 9 plus 68 end root end cell row blank equals cell square root of 81 end cell row blank equals 9 end table 

Maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight y minus left parenthesis negative 3 right parenthesis end cell equals cell equals negative 3 left parenthesis straight x minus 2 right parenthesis plus-or-minus 9 square root of 1 plus left parenthesis negative 3 right parenthesis squared end root end cell row cell straight y plus 3 end cell equals cell negative 3 straight x plus 6 plus-or-minus 9 square root of 1 plus 9 end root end cell row straight y equals cell negative 3 straight x plus 3 plus-or-minus 9 square root of 10 end cell end table 

Jadi, Persamaan garis singgung lingkaran straight L identical to straight x squared plus straight y squared minus 4 straight x plus 6 straight y equals 68 tegak lurus garis yeng melewati titik straight P left parenthesis negative 2 comma space 3 right parenthesis dan straight Q left parenthesis 4 comma space 5 right parenthesis 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 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 plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 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 9 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 10 end cell end table 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 05 Mei 2021

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