Perhatikan Soal UN SMA Tahun 2008 tentang LINGKARAN berikut ini. Tipe soal ini bisa ditemukan juga pada soal-soal UN SMA tahun sebelumnya.
Persamaan garis singgung melalui titik A(–2,–1) pada lingkaran x² + y² + 12x – 6y + 13 = 0 adalah ….
a. –2x – y – 5 = 0
b. x – y + 1 = 0
c. x + 2y + 4 = 0
d. 3x – 2y + 4 = 0
e. 2x – y + 3 = 0
Tipe soal ini dikatakan BONUS hanya karena saya berasumsi bahwa soal garis singgung pada lingkaran yang akan keluar pada UN SMA hanya pada kasus garis singgung yang melalui titik pada lingkaran (Dasar asumsi: syarat lulus UN kian tinggi, pemerintah juga takut banyak siswa yang tidak lulus, dan soal garis singgung pada titik diluar lingkaran cukup sulit bagi siswa kebanyakan, meskipun juga ada trik jawaban).
Penyelesaiannya:
Ubah persamaan lingkaran
x² + y² + 12x – 6y + 13 = 0 menjadi
x.x + y.y + 6 (2x) - 3(2y) + 13 = 0
x.x + y.y + 6(x+x) - 3(y+y) + 13 = 0
Berikutnya salah satu x dan y masing-masing ganti dengan -2 dan -1
(-2).x + (-1).y + 6(-2+x) - 3(-1+y) + 13 = 0
-2x - y - 12 + 6x + 3 - 3y + 13 = 0
4x - 4y + 4 = 0 (2 ruas bagi 4)
x - y + 1 = 0 (Jawaban B)
Semoga bermanfaat.
Tuesday, November 25, 2008
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