Question

Tentukan nilai m agar garis y=mx+1 menyinggung lingakaran x²+y²+2x+8y-8=0

Answer 1

Verified answer

Subtitusikan pers. garis y = mx + 1 ke pers. lingkaran.

x² + (mx + 1)² + 2x + 8(mx + 1) - 8 = 0
x² + 2x + m²x² + 2mx + 1 + 8mx + 8 - 8 = 0
(m² + 1)x² + (10m + 2)x + 1 = 0

a = (m² + 1)
b = (10m + 2)
c = 1

periksa nilai diskriminan.
syarat garis menyinggung adalah D = 0
jadi
D = b² - 4ac
D = (10m + 2)² - 4(m² + 1)
D = 100m² + 40m + 4 - 4m² - 4
D = 96m² + 40m

D = 0
96m² + 40m = 0
8m(12m + 5) = 0
m = 0   atau   m = -5/12