Answer:
(0, -4)
Step-by-step explanation:
The given relations tell you ...
p = 16/4 = 4
Then the equation of the parabola is ...
x^2 = -16y
It opens downward, so the focus is below the vertex. The distance between the vertex and the focus is p = 4, so the focus is (0, -4).
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The attached graph shows the parabola, along with its focus and directrix.
