Lingkaran dan Garis Singgung
P(3,-2) dan melalui (5,-1)
(x - 3)² + (y + 2)² = (5 - 3)² + (-1 + 2)²
(x - 3)² + (y + 2)² = 5
r = √5
garis
2x - y + 3 = 0
m1 = -a/b = -2/-1 = 2
Sejajar → m2 = m1 = 2
Persamaan garis singgung dg P = (a,b) = (3,-2) , r = √5 , dan m = 2 :
y - b = m(x - a) ± r√(1 + m²)
y - (-2) = 2(x - 3) ± √5 . √(1 + 2²)
y = 2x - 6 - 2 ± 5
y = 2x - 8 ± 5
PGSL_1 : y = 2x - 8 + 5 = 2x - 3
PGSL_2 : y = 2x - 8 - 5 = 2x - 13
Opsi : A
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Lingkaran dan Garis Singgung
P(3,-2) dan melalui (5,-1)
(x - 3)² + (y + 2)² = (5 - 3)² + (-1 + 2)²
(x - 3)² + (y + 2)² = 5
r = √5
garis
2x - y + 3 = 0
m1 = -a/b = -2/-1 = 2
Sejajar → m2 = m1 = 2
Persamaan garis singgung dg P = (a,b) = (3,-2) , r = √5 , dan m = 2 :
y - b = m(x - a) ± r√(1 + m²)
y - (-2) = 2(x - 3) ± √5 . √(1 + 2²)
y = 2x - 6 - 2 ± 5
y = 2x - 8 ± 5
PGSL_1 : y = 2x - 8 + 5 = 2x - 3
PGSL_2 : y = 2x - 8 - 5 = 2x - 13
Opsi : A