Question

What is the equation of the quadratic graph with a focus of (-4, 17/8) and a directrix of y=15/8

Answer 1

Yay

so
this is going to be
(x-h)^2=4p(y-k)

(h,k) is the vertex
p is the distance from the vertex to the focus and the vertex to directix

half of the distance between directix and focus is p
if the directix is above the focus, p is negative
if the directix is below the focus, p is positive
so

we see
y=15/8 is the directix
focus is above directix (p is positive)
it is 2/8 or 1/4 above it
so
half of 1/4 is 1/8
p=1/8
the vertex is 1/8 below vertex so it is it at (-4,16/8) or (-4,2)
the equation is
(x-(-4))^2=4(1/8)(y-2) or
(x+4)^2=4(1/8)(y-2) is the equation