SOLUTION: Determine the equation of a parabola, in standard form satisfying the given conditions: Focus (0,2); directrix y=-2

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Question 861647: Determine the equation of a parabola, in standard form satisfying the given conditions: Focus (0,2); directrix y=-2
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You have two choices. One is to use the basic developed formulaic knowledge about a parabola. The other is to use the distance formula to derive the equation which you want.

There is a general point on the parabola, (x, y). There is the line y=-2 and there is the focus (0,2). The variable point for the directrix line is (x,-2). Can you begin to draw this and see that the vertex will be (0,0) the origin? Continue to draw a representation of this parabola, since it will also help you in the use of the distance formula.

Distance parabola to focus = Distance parabola to directrix

sqrt%28%28x-0%29%5E2%2B%28y-2%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-%28-2%29%29%5E2%29; Does this equation make sense to you? When it makes sense, then simplify it, and work it into solved as y in terms of x.
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sqrt%28x%5E2%2B%28y-2%29%5E2%29=sqrt%280%2B%28y%2B2%29%5E2%29
x%5E2%2B%28y-2%29%5E2=%28y%2B2%29%5E2
x%5E2%2By%5E2-4y%2B4=y%5E2%2B4y%2B4
x%5E2-4y=4y-----this was a combination step,
4y=x%5E2-4y------symmetric property
8y=x%5E2
highlight%28y=%281%2F8%29x%5E2%29.