# Thread: Equation of a Parabola

1. ## Equation of a Parabola

I have to write the equation of a parabola with vertex (0,-6) and Focus (0,5). Since the two x terms are both 0, the parabola will be vertical. I think the equation will be:

(x-0)^2 = 4(?)(y-(-6))
x^2 = 4(?)(y+6)

I can't figure out what "p" should be because I have to multiply it by 4. I know "p" is the distance from the vertex to the focus. I think this might be 11. Is this correct? If not, how do I find it?

Thanks.

2. a parabola with an axis parallel to the y axis with vertex (h,k), focus (h,k + p), and directrix y = kp, with p being the distance from the vertex to the focus has eqn:

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

Yes, p is the distance from the vertex to the focus, which we can find in this case by taking:

y(focus)-y(vertex) = 5 - - 6 = 11

So yup, you got it all right!
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