Question 870622
The distance between F and any (x,y) is equal to the distance between the directrix (3,y) and (x,y).


{{{sqrt((x-4)^2+(y-0)^2)=sqrt((x-3)^2+(y-y)^2)}}}


{{{sqrt((x-4)^2+y^2)=sqrt((x-3)^2)}}}
{{{(x-4)^2+y^2=(x-3)^2}}}
{{{x^2-8x+16+y^2=x^2-6x+9}}}
{{{-8x+16+y^2=-6x+9}}}
{{{-2x+16+y^2=9}}}
{{{-2x=-y^2+9-16}}}
{{{2x=y^2+16-9}}}
{{{2x=y^2+7}}}
{{{highlight(x=(1/2)y^2+7/2)}}}