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In the figure below, F$(2,4)$ is the focus, P$(x,y)$ is a point on the parabola, and D$(x,2)$ is a point on the directrix.

If $FP = PX$ by definition of a parabola, what is the equation of this parabola?

A

$ y = (x-2)^2 + 3 $

B

$ y = (x-3)^2 + 2 $

C

$ y = \cfrac{1}{4}(x-2)^2 + 5 $

D

$ y = \cfrac{1}{4}(x-2)^2 + 3 $

E

$ y = \cfrac{1}{4}(x-2)^2 - 3 $

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