SOLUTION: The standard form equation of the parabola with focus at (2, 0), directrix y=-3.

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Question 1170537: The standard form equation of the parabola with focus at (2, 0), directrix y=-3.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Simply use the Distance Formula definition for Parabola, and put the equation into the final form you need.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given: the directrix is the line y=-3; the focus is at (2,0).

With that information, we know the parabola opens upward.

The distance from the directrix to the focus is 3 (from y=-3 to y=0).

The vertex is halfway between the directrix and the focus -- at (2,-1.5).

The vertex form of the equation is

y+=+%28%281%2F%284p%29%29%28x-h%29%5E2%29%2Bk

where (h,k) is the vertex and p is the directed distance from the directrix to the vertex, or from the vertex to the focus.

The given information leads us to a vertex at (2,-1.5) and a p value of 1.5. So the equation is

y+=+%28%281%2F6%29%28x-2%29%5E2%29-1.5