Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, 9).

First we write standard form that includes both vertex and focus. The formula goes like this:

(x-h) ^2 = 4*p * (y-k)

h and k are coordinates of vertex. since vertex is at beginning that means that h=k=0

p is focal lenght and in our case it is 9

expressing al of this we get:

x^2 = 4*9*y

x^2 = 36y

y = 1/36 * x^2