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Pertanyaan

Tentukan pusat dan jari-jari lingkaran dengan persamaan begin mathsize 14px style 4 x squared plus 4 y squared minus 8 x plus 12 y minus 3 equals 0 end style.

R. Azizatul

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

pusat lingkaran tersebut adalah begin mathsize 14px style open parentheses 1 comma negative 3 over 2 close parentheses end style dan jari-jarinya adalah begin mathsize 14px style 2 end style.

Pembahasan

Jika terdapat lingkaran dengan persamaan begin mathsize 14px style straight x squared plus straight y squared plus Ax plus By plus straight C equals 0 end style, maka pusat lingkaran tersebut adalah begin mathsize 14px style open parentheses negative straight A over 2 comma negative straight B over 2 close parentheses end style dan jari-jarinya adalah begin mathsize 14px style square root of open parentheses negative 1 half straight A close parentheses squared plus open parentheses negative 1 half straight B close parentheses squared minus straight C end root end style.

Sederhanakan dulu lingkaran dengan persamaan begin mathsize 14px style 4 x squared plus 4 y squared minus 8 x plus 12 y minus 3 equals 0 end style.

begin mathsize 14px style 4 x squared plus 4 y squared minus 8 x plus 12 y minus 3 equals 0 x squared plus y squared minus 2 x plus 3 y minus 3 over 4 equals 0 end style

- Tentukan pusat lingkaran

begin mathsize 14px style open parentheses straight a comma straight b close parentheses equals open parentheses negative straight A over 2 comma negative straight B over 2 close parentheses space space space space space space space equals open parentheses negative fraction numerator negative 2 over denominator 2 end fraction comma negative 3 over 2 close parentheses space space space space space space space space equals open parentheses 1 comma negative 3 over 2 close parentheses end style 

- Tentukan jari-jari lingkaran

begin mathsize 14px style straight r equals square root of open parentheses negative 1 half straight A close parentheses squared plus open parentheses negative 1 half straight B close parentheses squared minus straight C end root straight r equals square root of open parentheses negative 1 half cross times negative 2 close parentheses squared plus open parentheses negative 1 half cross times 3 close parentheses squared minus open parentheses negative 3 over 4 close parentheses end root straight r equals square root of open parentheses 1 close parentheses squared plus open parentheses negative 3 over 2 close parentheses squared plus 3 over 4 end root straight r equals square root of 1 plus 9 over 4 plus 3 over 4 end root straight r equals square root of 4 over 4 plus 9 over 4 plus 3 over 4 end root straight r equals square root of 16 over 4 end root straight r equals square root of 4 straight r equals 2 end style

Jadi, pusat lingkaran tersebut adalah begin mathsize 14px style open parentheses 1 comma negative 3 over 2 close parentheses end style dan jari-jarinya adalah begin mathsize 14px style 2 end style.

282

3.6 (3 rating)

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