Question

Can someone tell me if I am right?

I need to find the equation of a parabola. I am not sure if this is the correct way or if I have the correct answer.

Vertex at origin, focus is at (0,3)

Equation of parabola
vertex (0,0) focus (0,3)
focus (h,k+p)
(0,0+3)
y=0-3
directrix y=-3
a=(1/4)(p)
a=(1/4(-3))=(-1/12)
a=(-1/12) h=0 k=0
y=(-1/12)(x-0)^2+0
my answer is: y=(-1/12)(x^2)+0

Answer 1

shouldn't your parabola open upwards ?
your -1/12x^2.... makes it open down.

I do it this way:
let P(x,y) be any point on the parabola
by definition, the distance from P to the focal point is equal to the distance to the directrix --->
√(x^2 + (y-3)^2) = √(y+3)^2)

square both sides, and simplify to get

y = (1/12)x^2