Garis ax-2y+3=0 menyinggung lingkaran (x-1)^2+y^2=3, maka nilai a ....

Mapel Matematika
Bab Persamaan Lingkaran

ax - 2y + 3 = 0
-2y = -ax - 3
2y = ax + 3
y = (ax + 3)/2

(x - 1)^2 + y^2 = 3
x^2 - 2x + 1 + ((ax + 3)/2)^2 = 3
x^2 - 2x + 1 + ((ax)^2 + 6ax + 9)/4) = 3
4x^2 - 8x + 4 + (ax)^2 + 6ax + 9 = 12
4x^2 + (ax)^2 - 8x + 6ax + 1 = 0

Bersinggungan, maka D = 0
b^2 - 4ac = 0
(-8 + 6a)^2 - 4(4 + a^2)(1) = 0
64 - 96a + 36a^2 - 16 - 4a^2 = 0
32a^2 - 96a + 48 = 0
2a^2 - 6a + 3 = 0
(2a - 3)(a - 1) = 0

a = 3/2 atau a = 1