a) y = (1/8) ( x - 6)^2 + 4
We are working backwards, here
(y - 4) = (1/8) ( x - 6)^2
8(y - 4) = ( x - 6)^2 the vertex is ( 6, 4)
4p = 8 ⇒ p = 2
The parabola turns upward so the focus is ( 6 , 4 + p) = ( 6 , 4 + 2) = (6, 6)
And the directrix is y = 4 - p = 4 - 2 = 2 ⇒ y = 2