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Tentukan persamaan lingkaran yang melalui tiga titik berikut , , dan .

Tentukan persamaan lingkaran yang melalui tiga titik berikut begin mathsize 14px style straight P left parenthesis 2 comma space 0 right parenthesis end stylebegin mathsize 14px style straight Q left parenthesis 0 comma space minus 2 right parenthesis end style, dan Error converting from MathML to accessible text..

Jawaban:

Bentuk Umum persamaan lingkaran:

begin mathsize 14px style x squared plus y squared plus Ax plus By plus straight C equals 0 end style  

untuk: begin mathsize 14px style straight P left parenthesis 2 comma space 0 right parenthesis end style maka: 

Error converting from MathML to accessible text.        

Persamaan 1.

untuk: begin mathsize 14px style straight Q left parenthesis 0 comma space minus 2 right parenthesis end style maka:

Error converting from MathML to accessible text.  

Persamaan 2.

untuk Error converting from MathML to accessible text. maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 4 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus straight A left parenthesis 4 right parenthesis plus straight B left parenthesis negative 2 right parenthesis plus straight C end cell equals 0 row cell 16 plus 4 plus 4 straight A minus 2 straight B plus straight C end cell equals 0 row cell 4 straight A minus 2 straight B plus straight C end cell equals cell negative 20 end cell end table end style        

Persamaan 3.

Eliminasi begin mathsize 14px style straight A end style dari persamaan 1 dan persamaan 3, maka:

begin mathsize 14px style table row cell 2 straight A plus straight C equals negative 4 rightwards arrow end cell cell 4 straight A plus 2 straight C equals negative 8 end cell row cell 4 straight A minus 2 straight B plus straight C equals negative 20 rightwards arrow end cell cell 4 straight A minus 2 straight B plus straight C equals negative 20 minus end cell row blank cell 2 straight B plus straight C equals 12 end cell end table end style   

Persamaan 4.

Eliminasi begin mathsize 14px style straight B end style dari persamaan 2 dan persamaan 4:

begin mathsize 14px style table row cell negative 2 straight B plus straight C equals negative 4 end cell blank row cell 2 straight B plus straight C equals 12 space space space space plus end cell blank row cell 2 straight C equals 8 end cell blank row cell straight c equals 4 end cell blank end table end style   

Dari persamaan 1:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight A plus straight C end cell equals cell negative 4 end cell row cell 2 straight A plus 4 end cell equals cell negative 4 end cell row cell 2 straight A end cell equals cell negative 8 end cell row straight A equals cell negative 4 end cell end table end style 

Dari persamaan 2:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 straight B plus straight C end cell equals cell negative 4 end cell row cell negative 2 straight B plus 4 end cell equals cell negative 4 end cell row cell negative 2 straight B end cell equals cell negative 8 end cell row straight B equals 4 end table end style 

Bentuk umum persamaan lingkaran adalah:

begin mathsize 14px style straight x squared plus straight y squared plus Ax plus By plus straight C equals 0 rightwards arrow straight x squared plus straight y squared minus 4 straight x plus 4 straight y plus 4 equals 0 end style 

Jadi, Persamaan lingkaran yang melalui tiga titik berikut begin mathsize 14px style straight P left parenthesis 2 comma space 0 right parenthesis end stylebegin mathsize 14px style straight Q left parenthesis 0 comma space minus 2 right parenthesis end style, dan Error converting from MathML to accessible text. adalah size 14px x to the power of size 14px 2 size 14px plus size 14px y to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 4 size 14px y size 14px plus size 14px 4 size 14px equals size 14px 0 

 

 

 

 

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