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Diketahui dua lingkaran dengan persamaan x 2 + y 2 + 4 x − 6 y − 12 = 0 dan x 2 + y 2 − 12 x − 6 y + 20 = 0 . Persamaan lingkaran yang melalui titik A(4,2) adalah ...

Diketahui dua lingkaran dengan persamaan  dan . Persamaan lingkaran yang melalui titik A(4,2) adalah ...

 

  1. begin mathsize 14px style x squared plus y squared minus 2 x minus 6 y equals 0 end style  

  2. begin mathsize 14px style x squared plus y squared plus 2 x minus 6 y equals 0 end style  

  3. begin mathsize 14px style x squared plus y squared plus 2 x plus 6 y equals 0 end style  

  4. begin mathsize 14px style x squared plus y squared minus 2 x minus 6 y minus 1 equals 0 end style  

  5. begin mathsize 14px style x squared plus y squared plus 2 x minus 6 y plus 1 equals 0 end style   

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S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

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Pembahasan

Persamaan melalui titik (4,2), maka: Persamaan menjadi: Jadi, jawaban yang tepat adalah A.

begin mathsize 14px style L subscript 1 plus k times L subscript 2 equals 0 x squared plus y squared plus 4 x minus 6 y minus 12 plus k left parenthesis x squared plus y squared minus 12 x minus 6 y plus 20 equals 0 end style

Persamaan melalui titik (4,2), 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 2 right parenthesis squared plus 4 left parenthesis 4 right parenthesis minus 6 left parenthesis 2 right parenthesis minus 12 plus k left parenthesis left parenthesis 4 right parenthesis squared plus left parenthesis 2 right parenthesis squared minus 12 left parenthesis 4 right parenthesis minus 6 left parenthesis 2 right parenthesis plus 20 end cell equals 0 row cell 16 plus 4 plus 16 minus 12 minus 12 plus k open parentheses 16 plus 4 minus 48 minus 12 plus 20 close parentheses end cell equals 0 row cell 12 plus k left parenthesis negative 20 right parenthesis end cell equals 0 row k equals cell 3 over 5 end cell end table end style

Persamaan menjadi:

table attributes columnalign right center left columnspacing 0px end attributes row cell 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 plus size 14px 4 size 14px x size 14px minus size 14px 6 size 14px y size 14px minus size 14px 12 size 14px plus size 14px 3 over size 14px 5 size 14px left parenthesis 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 12 size 14px x size 14px minus size 14px 6 size 14px y size 14px plus size 14px 20 size 14px right parenthesis end cell size 14px equals size 14px 0 row cell 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 plus size 14px 4 size 14px x size 14px minus size 14px 6 size 14px y size 14px minus size 14px 12 size 14px plus size 14px 3 over size 14px 5 size 14px x to the power of size 14px 2 size 14px plus size 14px 3 over size 14px 5 size 14px y to the power of size 14px 2 size 14px 3 over size 14px 5 size 14px x to the power of size 14px 2 size 14px plus size 14px 3 over size 14px 5 size 14px y to the power of size 14px 2 size 14px left parenthesis size 14px 12 size 14px x size 14px right parenthesis size 14px minus size 14px 3 over size 14px 5 size 14px left parenthesis size 14px 6 size 14px y size 14px right parenthesis size 14px plus size 14px 12 end cell size 14px equals size 14px 0 row cell size 14px 8 over size 14px 5 size 14px x to the power of size 14px 2 size 14px plus size 14px 8 over size 14px 5 size 14px y to the power of size 14px 2 size 14px minus size 14px 16 over size 14px 5 size 14px x size 14px minus size 14px 48 over size 14px 5 size 14px y end cell size 14px equals size 14px 0 row cell 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 2 size 14px x size 14px minus size 14px 6 size 14px y end cell size 14px equals size 14px 0 end table

Jadi, jawaban yang tepat adalah A.

 

 

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