Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8.

Directrix y = 8
 It is a horizontal line  so the parabola is vertical. 
The focus (2, 4) lies below the directrix,
Therefore parabola opens downwards. 
vertex will be  halfway between focus and directrix, at (2, 6) 
focal length =p
= distance between focus and vertex
= 2 
y = (-1/(4p))(x - 2)² + 6 
y = (-1/8)(x - 2)² + 6
hope this helps