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Jika garis  menyinggung lingkaran , maka

Jika garis begin mathsize 14px style x minus y plus straight C equals 0 end style menyinggung lingkaran begin mathsize 14px style x squared plus y squared equals 25 end style, maka begin mathsize 14px style straight C equals.... end style 

  1. begin mathsize 14px style plus-or-minus 4 square root of 2 end style 

  2. begin mathsize 14px style plus-or-minus 5 square root of 2 end style 

  3. begin mathsize 14px style plus-or-minus 2 square root of 2 end style 

  4. begin mathsize 14px style plus-or-minus 3 square root of 2 end style 

  5. begin mathsize 14px style plus-or-minus square root of 2 end style 

Jawaban:

Persamaan garis singgung lingkaran

begin mathsize 14px style x minus y plus straight C equals 0 y equals x plus straight C equals 0 end style 

Subtitusi ke persamaan lingkaran

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus y squared end cell equals 25 row cell x squared plus open parentheses x plus straight C close parentheses squared end cell equals 25 row cell x squared plus x squared plus 2 straight C x plus straight C squared minus 25 end cell equals 0 row cell 2 straight x squared plus 2 Cx plus straight C squared minus 25 end cell equals 0 end table end style 

Syarat garis menyinggung lingkaran,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight D equals 0 row cell b squared minus 4 a c end cell equals 0 row cell open parentheses 2 straight C close parentheses squared minus 4 times 2 times open parentheses straight C squared minus 25 close parentheses end cell equals 0 row cell 4 straight C squared minus 8 straight C squared plus 200 end cell equals 0 row cell negative 4 straight C squared end cell equals cell negative 200 end cell row cell straight C squared end cell equals 50 row straight C equals cell plus-or-minus square root of 50 end cell row straight C equals cell plus-or-minus 5 square root of 2 end cell row blank blank blank row blank blank blank end table end style 

Jadi, jawaban yang tepat adalah B.

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