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?
a parabola with an axis parallel to the y axis with vertex (h,k), focus (h,k + p), and directrix y = k − p, 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!