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Agar lingkaran x2+y2−2x+8y+n=0 berjari-jari 6, n haruslah sama dengan ....

Pertanyaan

Agar lingkaran straight x squared plus straight y squared minus 2 straight x plus 8 straight y plus straight n equals 0 berjari-jari 6straight n haruslah sama dengan ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai straight n yang tepat adalah negative 19.

Pembahasan

Ingat kembali bentuk umum persamaan lingkaran:

straight x squared plus straight y squared plus Ax plus By plus straight C equals 0 titik space pusat rightwards arrow straight P open parentheses negative 1 half straight A comma space minus 1 half straight B close parentheses jari minus jari rightwards arrow 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 

lingkaran straight x squared plus straight y squared minus 2 straight x plus 8 straight y plus straight n equals 0 berjari-jari 6, maka:

space 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 space 6 equals square root of open parentheses negative 1 half open parentheses negative 2 close parentheses close parentheses squared plus open parentheses negative 1 half open parentheses 8 close parentheses close parentheses squared minus straight n end root space 6 equals square root of open parentheses 1 close parentheses squared plus open parentheses negative 4 close parentheses squared minus straight n end root space 6 equals square root of 1 plus 16 minus straight n end root space 6 equals square root of 17 minus straight n end root 6 squared equals open parentheses square root of 17 minus straight n end root close parentheses squared 36 equals 17 minus straight n space space straight n equals 17 minus 36 space space straight n equals negative 19 

Jadi, nilai straight n yang tepat adalah negative 19.

36

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Syifa Fauziyah

Makasih ❤️

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