Find the ve

Given equation of the parabola is y² = 8x + 8y

⇒ y² - 8y = 8x

⇒ y² - 8y + 16 = 8x + 16

⇒ (y - 4)² = 8(x + 2)

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

⇒ 4b = 8

⇒ b = 2

⇒ The vertex is (c, a) = (- 2, 4)

⇒ The focus is (b + c, a) =

⇒ The equation of the axis is y - a = 0 i.e, y - 4 = 0

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

⇒ Directrix is x - (-2) = -2

⇒ Directrix is x = -2 -2

⇒ Directrix is x = -4

⇒ Length of latus rectum is 4b = 8.