Find the equation of the parabola with the vertex at the origin and directrix y =5

Answer 1

The vertex is mid-way between the directrix and focal point:

D(0,5)

V(0,0)

F(0,y)

FV = VD = 1/4a = 5,
0 - y = 5,
Y = -5.

1/4a = 5,
Multiply both sides by 4a:
20a = 1,
a = 1/20.

Vertex Form: Y = a(x-h)^2 + k,
Y = 1/20(x-0)^2 + 0,
Eq: Y =(1/20)x^2