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Tentukan persamaan garis singgung lingkaran  yang ...

Tentukan persamaan garis singgung lingkaran begin mathsize 14px style x squared plus y squared equals 20 end style yang melalui titik begin mathsize 14px style open parentheses 6 comma space minus 2 close parentheses end style

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Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 20 row cell open parentheses 6 close parentheses squared plus open parentheses negative 2 close parentheses squared end cell equals 20 row cell 36 plus 4 end cell equals 20 row 40 greater than 20 end table end style

Karena begin mathsize 14px style 40 greater than 20 end style, maka diketahui bahwa titik begin mathsize 14px style open parentheses 6 comma space minus 2 close parentheses end style berada di luar lingkaran.

Langkah 1:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x plus y subscript 1 times y end cell equals cell r squared end cell row cell 6 x minus 2 y end cell equals 20 row cell 2 y end cell equals cell 6 x minus 20 end cell row y equals cell 3 x minus 10 end cell end table end style

Langkah 2:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 20 row cell x squared plus open parentheses 3 x minus 10 close parentheses squared end cell equals 20 row cell x squared plus 9 x squared minus 60 x plus 100 end cell equals 20 row cell 10 x squared minus 60 x plus 80 end cell equals 0 row cell x squared minus 6 x plus 8 end cell equals 0 row cell open parentheses x minus 4 close parentheses open parentheses x minus 2 close parentheses end cell equals 0 row x equals cell 4 logical or 2 end cell end table end style

Langkah 3:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x minus 10 end cell row y equals cell 3 open parentheses 4 close parentheses minus 10 end cell row y equals cell 12 minus 10 end cell row y equals 2 row blank blank blank row blank blank cell open parentheses 4 comma space 2 close parentheses end cell end table end style

Langkah 4:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x minus 10 end cell row y equals cell 3 left parenthesis 2 right parenthesis minus 10 end cell row y equals cell 6 minus 10 end cell row y equals cell negative 4 end cell row blank blank blank row blank blank cell left parenthesis 2 comma space minus 4 right parenthesis end cell end table end style

Garis singgung di titik begin mathsize 14px style open parentheses 4 comma space 2 close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x plus y subscript 1 times y end cell equals cell r squared end cell row cell 4 x plus 2 y end cell equals 20 row cell 2 x plus y end cell equals 10 end table end style

Garis singgung di titik begin mathsize 14px style open parentheses 2 comma space minus 4 close parentheses end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 times x plus y subscript 1 times y end cell equals cell r squared end cell row cell 2 x minus 4 y end cell equals 20 row cell x minus 2 y end cell equals 10 end table end style

Jadi, jawaban yang tepat adalah begin mathsize 14px style 2 x plus y equals 10 end style dan size 14px x size 14px minus size 14px 2 size 14px y size 14px equals size 14px 10.

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