Find the ve

Given equation of the parabola is x² + y = 6x - 14

⇒ x² - 6x = - y - 14

⇒ x² - 6y + 9 = - y - 5

⇒ (x - 3)² = - (y + 5)

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

⇒ 4b = 1

⇒

⇒ The vertex is (a, c) = (3, - 5)

⇒ The focus is (a, - b + c) =

⇒ The equation of the axis is x - a = 0 i.e, x - 3 = 0

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

⇒ Directrix is

⇒ The directrix is

⇒ Directrix is

⇒ Length of latus rectum is 4b = 1.