Posted by **Tim** on Wednesday, April 30, 2008 at 8:40pm.

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

- Algebra -
**Reiny**, Wednesday, April 30, 2008 at 9:09pm
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

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