Question 922281
Use the distance formula and the definition of a parabola; and then simplify the equation.


A variable set of points is (x,y), and the directrix is another variable set of points, (9,y).  The focus is the one specific given point (3,1).  Drawing a picture of this all may help.


Skipping most of the descriptive explanation,...
{{{highlight_green(sqrt((x-9)^2+(y-y)^2)=sqrt((x-3)^2+(y-1)^2))}}}.


If you understand that initial equation, then great!  You are understanding.  Now, just simplify it.