salah satu persamaan garis singgung lingkaran 2x+2y²-8x+16y+20=0 yang sejajar dengan garis 2x+6y-30=0 adalah... mohon dijawab secara rinci. terimakasih

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2x^2 + 2y^2 - 8x + 16y + 20 = 0 ......... bagi 2
x^2 + y^2 - 4x + 8y + 10 = 0 => A = -4, B = 8, C = 10
Pusat (a,b) = (-1/2 A, -1/2 B) = (-1/2 . -4, -1/2 . 8) = (2, -4)

Jari-jari = r = √(a^2 + b^2 - C) = √(2^2 + (-4)^2 - 10) = √(4 + 16 - 10) = √10

2x + 6y - 30 = 0 => m = -x/y = -2/6 = -1/3 karena sejajar m = -1/3 (m1 = m2)

Persamaan garis singgung lingkaran
y - b = m(x - a) ± r√(m^2 + 1)
y - (-4) = -1/3 (x - 2) ± √10 √((-1/3)^2 + 1)
y + 4 = -1/3 x + 2/3 ± √10 √(1/9 + 1)
y = -1/3 x + 2/3 - 4 ± √10 √(10/9)
y = -1/3 x - 10/3 ± 10/3 ...................... kali 3
3y = -x - 10 ± 10
x + 3y + 10 ± 10 = 0
1) x + 3y + 10 + 10 = 0 => x + 3y + 20 = 0
2) x + 3y + 10 - 10 = 0 => x + 3y = 0