Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.

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Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.

Mathematics
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  • phi
it helps to plot the directrix and the focus

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Other answers:

Well I know the vertex is (0,0)
  • phi
|dw:1436389666695:dw|
http://prntscr.com/7qfk7l
  • phi
yes the vertex is half way between them, so at (0,0) people label the vertex (h,k)
  • phi
and we know the parabola "surrounds" the focus so it looks (something) like |dw:1436389795339:dw|
  • phi
(y-k)= a(x-h)^2 with (h,k)= 0 and a will be negative y = ax^2 we need to find a
  • phi
I think people write it as \[ 4 p y = x^2 \] and p is the distance from the vertex to the focus (or vertex to the directrix) p=3 and negative because it's facing down -12y= x^2 so \[ y= -\frac{1}{12} x^2 \]
Thanks. I understand. I have a few more questions but i'll post new forms. Thanks again, @phi

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