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Lingkaran dengan persamaan  dirotasikan terhadap p...

Lingkaran dengan persamaan begin mathsize 14px style straight x squared plus straight y squared minus 6 straight x equals 4 end style dirotasikan terhadap pusat Error converting from MathML to accessible text. sebesar size 14px 270 size 14px degree searah putaran jarum jam.

Jawaban:

Dengan menerapkan konsep rotasi dengan titik pusat begin mathsize 14px style straight P left parenthesis straight a comma space straight b right parenthesis end style sebesar begin mathsize 14px style theta end style searah putaran jarum jam, yaitu:

begin mathsize 14px style open parentheses table row cell straight x apostrophe end cell row cell straight y apostrophe end cell end table close parentheses equals open parentheses table row cell cos space straight theta end cell cell negative sin space straight theta end cell row cell sin space straight theta end cell cell cos space straight theta end cell end table close parentheses times open parentheses table row cell straight x minus straight a end cell row cell straight y minus straight b end cell end table close parentheses plus open parentheses table row straight a row straight b end table close parentheses end style 

Dengan:

begin mathsize 14px style straight a equals 5 comma space straight b equals 0 space dan space straight theta equals 270 degree end style.

Misalkan begin mathsize 14px style left parenthesis straight x comma space straight y right parenthesis end style adalah titik-titik yang dilalui oleh lingkaran begin mathsize 14px style straight x squared plus straight y squared minus 6 straight x equals 4 end style maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell straight x apostrophe end cell row cell straight y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell cos space 270 degree end cell cell negative sin space 270 degree end cell row cell sin space 270 degree end cell cell cos space 270 degree end cell end table close parentheses times open parentheses table row cell straight x minus 5 end cell row cell straight y minus 0 end cell end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 0 cell negative left parenthesis negative 1 right parenthesis end cell row cell negative 1 end cell 0 end table close parentheses times open parentheses table row cell straight x minus 5 end cell row straight y end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 0 1 row cell negative 1 end cell 0 end table close parentheses times open parentheses table row cell straight x minus 5 end cell row straight y end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row cell 0 times left parenthesis straight x minus 5 right parenthesis plus 1 times left parenthesis straight y right parenthesis end cell row cell negative 1 left parenthesis straight x minus 5 right parenthesis plus 0 times straight y end cell end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row straight y row cell negative 1 left parenthesis straight x minus 5 right parenthesis end cell end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row straight y row cell negative straight x plus 5 end cell end table close parentheses plus open parentheses table row 5 row 0 end table close parentheses end cell row blank equals cell open parentheses table row cell straight y plus 5 end cell row cell negative straight x plus 5 end cell end table close parentheses end cell end table end style 

Dengan konsep kesamaan matriks diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell straight x apostrophe end cell row cell straight y apostrophe end cell end table close parentheses end cell equals cell open parentheses table row cell straight y plus 5 end cell row cell negative straight x plus 5 end cell end table close parentheses end cell row cell straight x apostrophe end cell equals cell straight y plus 5 end cell row cell straight x apostrophe minus 5 end cell equals straight y row straight y equals cell straight x apostrophe minus 5 end cell row cell straight y apostrophe end cell equals cell negative straight x plus 5 end cell row straight x equals cell negative straight y apostrophe plus 5 end cell end table end style  

maka bayangan begin mathsize 14px style straight x squared plus straight y squared minus 6 straight x equals 4 end style oleh rotasi tersebut adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis negative straight y apostrophe plus 5 right parenthesis squared plus left parenthesis straight x apostrophe minus 5 right parenthesis squared minus 6 left parenthesis negative straight y apostrophe plus 5 right parenthesis end cell equals 4 row cell straight y apostrophe squared minus 10 straight y apostrophe plus 25 plus straight x apostrophe squared minus 10 straight x apostrophe plus 25 plus 6 straight y apostrophe minus 30 end cell equals 4 row cell straight x apostrophe squared plus straight y apostrophe squared minus 10 straight x apostrophe minus 4 straight y apostrophe plus 20 end cell equals 4 row cell straight x apostrophe squared plus straight y apostrophe squared minus 10 straight x apostrophe minus 4 straight y apostrophe plus 16 end cell equals 0 row blank blank blank end table end style 

Jadi, Bayangan lingkaran begin mathsize 14px style straight x squared plus straight y squared minus 6 straight x equals 4 end style jika dirotasikan terhadap pusat Error converting from MathML to accessible text. sebesar size 14px 270 size 14px degree searah putaran jarum jam adalah begin mathsize 14px style straight x squared plus straight y squared minus 10 straight x minus 4 straight y plus 16 equals 0 end style.

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