Given equation of the parabola is y² - 4y - 3x + 1 = 0

⇒ y² - 4y = 3x - 1

⇒ y² - 4y + 4 = 3x + 3

⇒ (y - 2)² = 3(x + 1)

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

⇒ 4b = 3

⇒

⇒ The vertex is (c, a) = (- 1, 2)

⇒ The focus is (b + c, a) =

⇒ The equation of the axis is y - a = 0 i.e, y - 2 = 0

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

⇒ Directrix is

⇒ Directrix is

⇒ Directrix is

⇒ Length of latus rectum is 4b = 3.