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Given equation of the parabola is x² - 4x - 8y + 12 = 0

⇒ x² - 4x + 12 = 8y

⇒ x² - 4x + 4 = 8y - 8

⇒ (x - 2)² = 8(y - 1)

Comparing with the standard form of parabola (x - a)² = 4b(y - c) we get,

⇒ 4b = 8

⇒ b = 2

⇒ The equation of the directrix is y - c = - b

⇒ Directrix is y - 1 = - 2

⇒ Directrix is y = - 2 + 1

⇒ Directrix is y = - 1

∴The equation of the directrix is y = - 1.