There is an error because the directrix must be perpendicular,
not parallel, to the line through the foci and the vertex.
Directrix x=9square root of 5 /5 +2
That is a vertical directix, and
center at (2,-6) and one of vertices at (2,-4).
That says the line through these points is also vertical. One of
these is vertical and the other horizontal. They cannot both be
vertical. You may restate your peoblem correctly on the thank-you
note form, and I will respond by email.
Edwin