Question 862102
The given directrix indicates the line of symmetry is horizontal.  Having the focus (1, 4) and the directrix x=-3, means you can use the Distance Formula according to the definition for a parabola and derive this equation.  The parabola is some variable set of points, (x,y).  The directrix is some variable set of points, (-3, y).  Drawing a picture will help.  


Starting with your symbolic statement,
{{{highlight_green(sqrt((x-1)^2+(y-4)^2)=sqrt((x-x)^2+(y-(-3))^2))}}}, using Distance Formula;
Simplify that and form your result into x on one side, and the expression of y on the other side.