I need help and the steps on how to solve this

Question

Find the directrix for the parabola

Answer 1

y = a(x - h)² + k

y = (1/16)(x - 2)² - 1)

vertex at (h, k) or (2, -1)

Directrix:

y = k - p

p = 1 / 4a

p = 1 / (4)(1/16)

p = 4

y = -1 - 4

y = -5

Answer 2

right off we see the vertex is (2,-1). at x=2 the distance from vertex to focus and vertex to directix does not involve x when at the vertex.

very generally when it is set that any point distance from focus and directix are equal,

the equation is ((x-x_f)²)/(y_f-y_d)=y-(y_f+y_d), a parabola.

y_f=y focus coodinate

y_d= y directix coordinate

two equations simultaneous

y_f+y_d=-1

y_f-y_d=16

y_d=-17/2 straight line horizopntal to x-axis