SOLUTION: Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4). choices below y = negative one divided by four x2 y2 = -4x

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Question 1135978: Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).
choices below
y = negative one divided by four x2

y2 = -4x

y2 = -16x

y = negative one divided by sixteen x2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the parabola with
a vertex at the origin: (0,0)
and a focus at :(0,+-4).

the absolute value of p+is the distance between the vertex and the focus :
The focus is at (h, k+%2B+p)
=>k+%2B+p=-4
=>0+%2B+p=-4
=>p+=-4
Since this is a "downward" parabola, then the x part gets squared, rather than the y part. So the conics form of the equation must be:
4p%28y-+y%5B1%5D%29+=+%28x+-x%5B1%5D%29%5E2
+4%28-4%29%28y-+0%29+=+%28x+-0%29%5E2
-16y=+x%5E2
y+=+-%281%2F16%29x%5E2+