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Rangkuman Lingkaran Persamaaan lingkaran Pengertian lingkaran adalah tempat kedudukan titik-titik yang berjarak sama atau tetap terhadap titik tertentu. Yang dimaksud titik tertentu adalah pusat lingkaran sedangkan jarak yang tetap adalah jari-jari lingkaran. Beberapa persamaan lingkaran: Sehingga, untuk menentukan persamaan lingkaran, langkah yang harus dilakukan adalah: • Menentukan pusat dan jari—jarinya • Menentukan persamaan lingkaran yang sesuai (x-a) 2 + (y – b) 2 = r 2 atau x 2 + y 2 = r 2 Persamaan Jarak pada Lingkaran • Jarak titik (x 1, y 1) ke titik (x 2, y 2) • Jarak titik (x 1, y 1) ke garis Ax + By + C = 0 Persamaan Garis Singgung Garis yang memotong lingkaran di satu titik disebut garis singgung. Ada tiga hal yang menentukan, yaitu: • Apabila diketahui titik pada lingkaran Terdapat titik (x 1, y 1) pada lingkaran, maka persamaan harus diubah sebagai berikut: Persamaannya menjadi: • Apabila diketahui titik di luar lingkaran • Tentukan persamaan garis kutub (polar) dari titik A(x 1, y 1) terhadap lingkaran. • Melalui titik potong antara garis kutub • Tentukan persamaan garis singgung melalui titik potong garis kutub (polar) dan • Diketahui Gradien Apabila diketahui titik () dengan gradien m pada lingkaran. Kedudukan Dua Lingkaran Apabila jarak antara pusat-pusat lingkaran kita sebut d, untuk r 1 dan r 2 merupakan jari-jari pada masing-masing kedua lingkaran, maka kedua lingkaran akan: • Saling lepas, sehingga d ˃ r 1 + r 2 • Saling bersinggungan di dalam lingkaran, sehingga d =|r 1 – r 2| • Saling bersinggungan di luar lingkaran, sehingga d = r 1 + r 2 • Saling berpotongan, sehingga|r 1 – r 2|. 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