Persamaan Lingkaran dan Irisan Dua Lingkaran | Matematika Kelas X
Lingkaran dapat ditemukan di kehidupan sehari-hari. Penerapannya sangat berguna, misalnya saja penggunaan roda, dan banyak mesin lainnya yang menerapkan bentuk lingkaran ini agar bisa berotasi dan bergerak.
Pada materi kali ini akan dibahas mengenai lingkaran.
1. Persamaan Lingkaran
Persamaan lingkaran dengan pusat O (0,0) dan jari-jari r, adalah:
x² + y² = r²
Persamaan lingkaran dengan pusat A (a,b) dan jari-jari r, adalah:
(x - a)² + (y-b)² = r²
Bentuk umum persamaan lingkaran
x² + y² + Ax + By + C = 0
A, B, dan C adalah bilangan real
Pusatnya : P (-1/2 A, -1/2B) dan jari-jari
2. PERSAMAAN GARIS SINGGUNG PADA LINGKARAN
1. Persamaan Garis Singgung Melalui Titik pada Lingkaran
a. Persamaan garis singgung melalui titik P(x1, y1) pada lingkaran x2 + y2 = r 2 adalah xx1 + yy1 = r2 .
b. Persamaan garis singgung melalui titik P(x1, y1) pada lingkaran
(x - a)2 + (y - b)2 = r2 adalah (x - a)(x1 - a) + (y - b)(y - y1) = r2
c. Persamaan garis singgung melalui titik P(x1, y1) pada lingkaran adalah
x2 + y2 + Ax + By + C = 0 xx1 + yy1 + A(x + x1) + B(y + y1) + C = 0.
2. Persamaan Garis Singgung dengan Gradien Tertentu
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)
3. Rumus-rumus persamaan lingkaran
Contoh soal:
Nah, itulah pembahasan materi pembelajaran matematika kelas sepuluh tentang persamaan lingkaran dan irisan dua lingkaran. Apabila ada pertanyaan atau pendapat yang ingin disampaikan, Anda bisa langsung serukan di kolom komentar di bawah yaaaah…
Anda juga dapat menghubungi kami di 085810779967 atau Head Office kami 021-77844897 di setiap hari Senin s.d Jumat pada pukul 09.00-17.00.
Anda bisa menemui kami langsung di kantor Ocean Terrace Residence Blok E1 No.1 Jalan Tole Iskandar, Tirtajaya, Kec. Sukmajaya, Kota Depok, Jawa Barat. Latis Education melayani les privat untuk semua wilayah di Indonesia.