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Tentukan persamaan lingkaran jika berpusat di  dan...

Tentukan persamaan lingkaran jika berpusat di Error converting from MathML to accessible text. dan menyinggung garis begin mathsize 14px style straight x minus straight y plus 2 equals 0 end style.

Jawaban:

Dengan menerapkan konsep jarak titik terhadap garis.

jarak titik pusat terhadap garis singgung adalah radius.

maka:

begin mathsize 14px style straight r equals fraction numerator open vertical bar aA plus bB plus straight C close vertical bar over denominator square root of straight A squared plus straight B squared end root end fraction end style  

dengan

begin mathsize 14px style left parenthesis straight a comma space straight b right parenthesis equals left parenthesis 3 comma space 2 right parenthesis end style 

Persamaan garis singgung: begin mathsize 14px style straight x minus straight y plus 2 equals 0 end style maka begin mathsize 14px style straight A equals 1 comma space straight B equals negative 1 comma space straight C equals 2 end style, sehingga diperoleh:

Error converting from MathML to accessible text. 

Jadi persamaan lingkaran adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight x minus straight a right parenthesis squared plus left parenthesis straight y minus straight b right parenthesis squared end cell equals cell straight r squared space end cell row cell left parenthesis straight x minus 3 right parenthesis squared plus left parenthesis straight y minus 2 right parenthesis squared end cell equals cell left parenthesis 3 over 2 square root of 2 right parenthesis squared space end cell row cell straight x squared minus 6 straight x plus 9 plus straight y squared minus 4 straight y plus 4 end cell equals cell 9 over 4 times 2 end cell row cell straight x squared plus straight y squared minus 6 straight x minus 4 straight y plus 13 end cell equals cell 9 over 2 end cell row cell 2 straight x squared plus 2 straight y squared minus 12 straight x minus 8 straight y plus 26 end cell equals 9 row cell 2 straight x squared plus 2 straight y squared minus 12 straight x minus 8 straight y plus 26 minus 9 end cell equals 0 row cell 2 straight x squared plus 2 straight y squared minus 12 straight x minus 8 straight y plus 17 end cell equals 0 end table end style  

Jadi, Persamaan lingkaran yang berpusat di Error converting from MathML to accessible text. dan menyinggung garis begin mathsize 14px style straight x minus straight y plus 2 equals 0 end style adalah begin mathsize 14px style 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 squared 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 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight y end table squared 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 12 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 straight y 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 17 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 end style.

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