SOLUTION: find the equation of a parabola with the focus (-1,-4) and directrix y=-3

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Question 456555: find the equation of a parabola with the focus (-1,-4) and directrix y=-3
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of the parabola has the form
4a%28y+-+k%29+=+%28x+-+h%29%5E2
From the given, the x-coordinate of the vertex must be -1. The y-coordinate must be midway between y = -3 and y = -4. Hence, k = -7/2.
Also, a = -4 - (-7/2) = -1/2, the directed distance from the focus to the vertex.
==> 4%2A%28-1%2F2%29%2A%28y+--7%2F2%29+=+%28x--1%29%5E2, or
-2%28y%2B7%2F2%29+=+%28x%2B1%29%5E2