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Persamaan lingkaran yang diameternya merupakan garis yang menghubungkan titik A(4, −1) dan B(−2, −3) adalah ....

Pertanyaan

Persamaan lingkaran yang diameternya merupakan garis yang menghubungkan titik straight A open parentheses 4 comma space minus 1 close parentheses dan straight B open parentheses negative 2 comma space minus 3 close parentheses adalah ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Pembahasan

Ingat kembali cara menentukan titik pusat dan jari-jari antara 2 titik:

straight P open parentheses straight a comma space straight b close parentheses equals open parentheses fraction numerator straight x subscript 1 plus straight x subscript 2 over denominator 2 end fraction comma space fraction numerator straight y subscript 1 plus straight y subscript 2 over denominator 2 end fraction close parentheses straight r equals 1 half square root of open parentheses straight x subscript 2 minus straight x subscript 1 close parentheses squared plus open parentheses straight y subscript 2 minus straight y subscript 1 close parentheses squared end root  

Diketahui titik straight A open parentheses 4 comma space minus 1 close parentheses dan straight B open parentheses negative 2 comma space minus 3 close parentheses, maka:

- Menentukan Titik Pusat

straight P open parentheses straight a comma space straight b close parentheses equals open parentheses fraction numerator straight x subscript 1 plus straight x subscript 2 over denominator 2 end fraction comma space fraction numerator straight y subscript 1 plus straight y subscript 2 over denominator 2 end fraction close parentheses straight P open parentheses straight a comma space straight b close parentheses equals open parentheses fraction numerator 4 plus open parentheses negative 2 close parentheses over denominator 2 end fraction comma space fraction numerator negative 1 plus open parentheses negative 3 close parentheses over denominator 2 end fraction close parentheses straight P open parentheses straight a comma space straight b close parentheses equals open parentheses 2 over 2 comma space fraction numerator negative 4 over denominator 2 end fraction close parentheses straight P open parentheses straight a comma space straight b close parentheses equals open parentheses 1 comma space minus 2 close parentheses 

- Menentukan Jari-jari

straight r equals 1 half square root of open parentheses straight x subscript 2 minus straight x subscript 1 close parentheses squared plus open parentheses straight y subscript 2 minus straight y subscript 1 close parentheses squared end root straight r equals 1 half square root of open parentheses negative 2 minus 4 close parentheses squared plus open parentheses negative 3 minus open parentheses negative 1 close parentheses close parentheses squared end root straight r equals 1 half square root of open parentheses negative 6 close parentheses squared plus open parentheses negative 2 close parentheses squared end root straight r equals 1 half square root of 36 plus 4 end root straight r equals 1 half square root of 40 straight r equals 1 half cross times 2 square root of 10 straight r equals square root of 10 

Sehingga:

space space space space space space open parentheses straight x minus straight a close parentheses squared plus open parentheses straight y minus straight b close parentheses squared equals straight r squared open parentheses straight x minus 1 close parentheses squared plus open parentheses straight y minus open parentheses negative 2 close parentheses close parentheses squared equals open parentheses square root of 10 close parentheses squared space space space space space space open parentheses straight x minus 1 close parentheses squared plus open parentheses straight y plus 2 close parentheses squared equals 10 

Jadi, persamaan lingkarannya adalah open parentheses straight x minus 1 close parentheses squared plus open parentheses straight y plus 2 close parentheses squared equals 10.

 

231

3.0 (3 rating)

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Tentukan persamaan lingkaran jika diketahui: b. pusat pada garis x−y−1=0, melalui titik (0,0), dan berjari-jari 5​.

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