Question 1190795
Definition for Parabola using the Distance Formula!
The focus is on the other side of the vertex than the directrix.


Starting a graph you can identify directrix as y=6, or (x,6).  All values for x.


Distance between (x,y) and (5,2) equals distance between (x,y) and (x,6).

{{{sqrt((x-5)^2+(y-2)^2)=sqrt((x-x)^2+(y-6)^2)}}}
Simplify and put into whatever form you need.

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{{{(x-5)^2=y^2-12y+36-(y^2-4y+4)}}}

{{{(x-5)^2=-8y+32}}}

{{{highlight((x-5)^2=-8(y-4))}}}