Question

Agar garis y = x + n menyinggung lingkaran x^2 + y^2 - 6x - 2y + 2 = 0 maka nilai n

Answer 1

Syarat menyinggung D = 0
y = x + n sub ke ling
x^2 + (x+n)^2 - 6x + 2(x+n) +2 = 0
x^2 +x^2 + 2xn +n^2 - 6x + 2x + 2n + 2 = 0
2 x^2 + (2n -4) x + (2n+2) = 0
D = 0
(2n-4)^2 - 4(2)(2n+2) = 0
4n^2 - 16n + 16 - 16n - 16 =0
4n^2 -32n = 0
4n(n-8) = 0
n = 0 atau  n = 8