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

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Question 983231: Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition of a parabola and the distance formula.

Distance of points (x,y) are equally distant from (0,-2) as from (x,2).
sqrt%28%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-2%29%5E2%29
sqrt%28x%5E2%2B%28y%2B2%29%5E2%29=sqrt%280%2B%28y-2%29%5E2%29
x%5E2%2B%28y%2B2%29%5E2=%28y-2%29%5E2
x%5E2%2By%5E2%2B4y%2B4=y%5E2-4y%2B4
x%5E2%2B4y=-4y
x%5E2=-4y-4y
-8y=x%5E2, not yet standard form but useful for understanding the derivation.
highlight%28y=-%281%2F8%29x%5E2%29-----standard form.

That can also be shown as y=-%281%2F8%29%28x-0%29%5E2%2B0 to help show how you can read the standard form equation. Vertex is (h,k) same as (0,0). The parabola has y-axis as its axis of symmetry and the parabola opens downward; the vertex is a maximum point.