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Kedudukan garis begin mathsize 14px style 3 x plus y minus 3 equals 0 end style dan lingkaran begin mathsize 14px style x squared plus y squared equals 9 end style adalah ...

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 garis begin mathsize 14px style 3 x plus y minus 3 equals 0 end style memotong begin mathsize 14px style x squared plus y squared equals 9 end style.

Pembahasan

Mencari diskriminan dengan mensubstitusi begin mathsize 14px style 3 x plus y minus 3 equals 0 end style ke begin mathsize 14px style x squared plus y squared equals 9 end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus y minus 3 end cell equals 0 row y equals cell 3 minus 3 x end cell row blank blank blank row cell x squared plus open parentheses 3 minus 3 x close parentheses squared end cell equals 9 row cell x squared plus open parentheses 9 minus 18 x plus 9 x squared close parentheses end cell equals 9 row cell x squared plus 9 minus 18 x plus 9 x squared minus 9 end cell equals 0 row cell 10 x squared minus 18 x end cell equals 0 end table end style 

didapat nilai begin mathsize 14px style a equals 10 comma space b equals ​ minus 18 comma space c equals 0 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row D equals cell b squared minus 4 a c end cell row blank equals cell open parentheses negative 18 close parentheses squared minus 4 open parentheses 10 close parentheses open parentheses 0 close parentheses end cell row D equals 324 row D greater than 0 end table end style 

Karena begin mathsize 14px style D greater than 0 end style, maka garis begin mathsize 14px style 3 x plus y minus 3 equals 0 end style memotong begin mathsize 14px style x squared plus y squared equals 9 end style.

Jadi, garis begin mathsize 14px style 3 x plus y minus 3 equals 0 end style memotong begin mathsize 14px style x squared plus y squared equals 9 end style.

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Tentukan kedudukan garis y=3x+1 terhadap lingkaran-lingkaran berikut. b. (x−1)2+(y−2)2=4

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