SOLUTION: write the equation of a parabola with a focus at (0,1) and a directrix of y=-1

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Question 864330: write the equation of a parabola with a focus at (0,1) and a directrix of y=-1
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
One way is try the definition of a parabola and the use of the Distance Formula.

Cutting past all the instructive description, the directrix is all points, (x,-1). The parabola is a variable set of points, (x,y):

sqrt%28%28x-0%29%5E2%2B%28y-1%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-%28-1%29%29%5E2%29
x%5E2%2B%28y-1%29%5E2=0%2B%28y%2B1%29%5E2
x%5E2%2By%5E2-2y%2B1=y%5E2%2B2y%2B1
x%5E2-2y=2y
highlight%28x%5E2=4y%29
OR
highlight%28y=%281%2F4%29x%5E2%29