Question 864330
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((x-0)^2+(y-1)^2)=sqrt((x-x)^2+(y-(-1))^2)}}}
{{{x^2+(y-1)^2=0+(y+1)^2}}}
{{{x^2+y^2-2y+1=y^2+2y+1}}}
{{{x^2-2y=2y}}}
{{{highlight(x^2=4y)}}}
OR
{{{highlight(y=(1/4)x^2)}}}