Jawaban:

koordinat titik pusat dan jari-jari lingkaran tersebut berturut-turut adalah open parentheses 2 comma negative 1 close parentheses space dan space 3

Penjelasan dengan langkah-langkah:

Diketahui persamaan lingkaran x squared plus y squared minus 4 x plus 2 y minus 4 equals 0 dimana A equals negative 4 comma space B equals 2 comma space dan space C equals negative 4.

Jika persamaan lingkaran x squared plus y squared plus A x plus B y plus C equals 0, maka pusatnya open parentheses negative 1 half A comma negative 1 half B close parentheses dan jari-jarinya square root of 1 fourth A squared plus 1 fourth B squared minus C end root.

Titik pusat lingkaran x squared plus y squared minus 4 x plus 2 y minus 4 equals 0:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 1 half A comma negative 1 half B close parentheses end cell equals cell open parentheses negative 1 half open parentheses negative 4 close parentheses comma negative 1 half open parentheses 2 close parentheses close parentheses end cell row blank equals cell open parentheses 4 over 2 comma negative 2 over 2 close parentheses end cell row blank equals cell open parentheses 2 comma negative 1 close parentheses end cell end table

Maka titik pusatnya adalah open parentheses 2 comma negative 1 close parentheses.

Jari-jari lingkaran x squared plus y squared minus 4 x plus 2 y minus 4 equals 0:

table attributes columnalign right center left columnspacing 0px end attributes row r equals cell square root of 1 fourth A squared plus 1 fourth B squared minus C end root end cell row blank equals cell square root of 1 fourth open parentheses negative 4 close parentheses squared plus 1 fourth open parentheses 2 close parentheses squared minus open parentheses negative 4 close parentheses end root end cell row blank equals cell square root of 16 over 4 plus 4 over 4 plus 4 end root end cell row blank equals cell square root of 4 plus 1 plus 4 end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table

Maka jari-jarinya adalah 3.