Hello peekybooyouYou're right so far. You have used the fact that the parabola has vertex at and a vertical axis of symmetry. You've replaced by and by to give a parabola whose vertex is at .

Now you need to use the fact that the parabola has directrix .

If in the coordinates, the directrix is , in the coordinates it is

So in coordinates the equation is ; in coordinates it is

Grandad