Jawab:
(a.)  y = 2
(b.)  =  (-1, 2)  dan (-5, 2)
(c.)  y = -½ x + ³/₂  dan  y = ½ x + ⁹/₂

Penjelasan:
Diketahui pers lingkaran
x² + y² + 6x + 4y - 7 = 0
x² + y² + Ax + By + C = 0
A = 6, B = 4, C = -7

Jari-jari kuadrat (r²)
4r² = A² + B² - 4C
4r² = 6² + 4² - 4(-7)
4r² = 36 + 16 + 28
4r² = 80
r² = 80/4
-->  r² = 20

Titik pusat = (-A/2, -B/2)
Titik pusat = (-6/2, -4/2)
Titik pusat = (-3, -2)
-->  p = -3, q = -2

Garis singgungnya melalui titik (-3, 3)
sehingga x₀ = -3, y₀ = 3

(a.) Pers garis polar
(x₀ - p)(x - p) + (y₀ - q)(y - q) = r²
(-3-(-3))(x-(-3)) + (3-(-2))(y-(-2)) = 20
(-3+3)(x+3) + (3+2)(y+2) = 20
(3+2)(y+2) = 20
5(y+2) = 20
5y + 10 = 20
5y = 20-10
5y = 10
y = 10/5
y = 2

(b.) Titik-titik singgung
Cari nilai x
x² + y² + 6x + 4y - 7 = 0
x² + 2² + 6x + 4(2) - 7 = 0
x² + 4 + 6x + 8 - 7 = 0
x² + 6x + 5 = 0
(x + 1)(x + 5) = 0
x = -1, atau x = -5
Titik singgung = (x₁, y₁) dan (x₂, y₂)
Titik singgung = (-1, 2)  dan (-5, 2)

(c.) Persamaan garis singgung
bentuk y = mx + k

-->  Garis (I)
Cari gradien (m)
m = (y₀-y₁)/(x₀-x₁)
m = (3-2)/(-3-(-1))
m = (3-2)/(-3+1)
m = 1/(-2)
m = -½
Cari persamaannya
y-y₀ = m(x-x₀)
y-3 = -½ (x-(-3))
y-3 = -½ x - ³/₂
y = -½ x - ³/₂ + 3
y = -½ x - ³/₂ + ⁶/₂
y = -½ x + ³/₂

-->  Garis ke-(II)
Cari gradien (m)
m = (y₀-y₂)/(x₀-x₂)
m = (3-2)/(-3-(-5))
m = (3-2)/(-3+5)
m = 1/2
m = ½
Cari persamaannya
y-y₀ = m(x-x₀)
y-3 = ½ (x-(-3))
y-3 = ½ x + ³/₂
y = ½ x + ³/₂ + 3
y = ½ x + ³/₂ + ⁶/₂
y = ½ x + ⁹/₂

Pers garis singgung ->
y = -½ x + ³/₂  dan
y = ½ x + ⁹/₂

(Xcvi)