anonymous
  • anonymous
Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
myininaya
  • myininaya
Hey.
myininaya
  • myininaya
so I like to a do a rough drawing to first figure out if my p is going to be negative or positive and where my vertex is going to be.

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anonymous
  • anonymous
it should be positive, just making a mental sketch
myininaya
  • myininaya
p is negative if the directrix is above the focus. p is positive if the directrix is below the focus.
myininaya
  • myininaya
The vertex is halfway between the vertex and the directrix.
anonymous
  • anonymous
0,0
myininaya
  • myininaya
right
myininaya
  • myininaya
and also right on the first thing
myininaya
  • myininaya
so we just need to figure out what p is
myininaya
  • myininaya
p is the distance between the focus and the vertex
myininaya
  • myininaya
or you can look at it as the distance between the vertex and the directrix
anonymous
  • anonymous
so 6
myininaya
  • myininaya
\[4py=x^2 \] is what we had and we knew p was going to be postive because focus was above directrix and yep just replace p with 6
anonymous
  • anonymous
so 24y=x²
myininaya
  • myininaya
yep or you can write it as y=x^2/24 I just divided 24 on both sides
anonymous
  • anonymous
my answer is y = 1/24x²
myininaya
  • myininaya
that sounds good too
anonymous
  • anonymous
yes, My answer choice is written in the form I wrote it in
anonymous
  • anonymous
thanks

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