Question 966781
So many questions of this kind are asked.  Use the definition of a parabola and the distance formula.  Simplify the equation resulting.


Directrix is (x,-2)


{{{sqrt((x-0)^2+(y-2)^2)=sqrt((x-x)^2+(y-(-2))^2)}}}




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Simplification steps:


{{{sqrt(x^2+(y-2)^2)=sqrt(0+(y+2)^2)}}}

{{{sqrt(x^2+(y-2)^2)=sqrt((y+2)^2)}}}

Square both sides:

{{{x^2+(y-2)^2=(y+2)^2}}}

{{{x^2+y^2-4y+4=y^2+4y+4}}}

{{{x^2-4y+4=4y+4}}}

{{{x^2=4y+4+4y-4}}}

{{{highlight(x^2=8y)}}}
OR
{{{highlight(y=(1/8)x^2)}}}