To find the focus, you need to know that the latus rectum is equal to "4p" when the parabola equation is written in this form:
4p(x-h) = (y-k)^2
"p" is the distance between the directrix and the vertex, as well as the distance between the vertex and the focus.
This a "sideways" parabola, since the axis is y=-5 (horizontal line).
You know the vertex is "p" units away from the directrix, and in this case, p=2.25 (since 4p = 4*2.25 = 9). So the vertex is at the point (8.25, -5). (8.25 is 6 + 2.25 -- the directrix plus "p")
So the equation of the parabola is 9(x-8.25) = (y+5)^2 using the form above.
Equation: 9(x-8.25) = (y+5)^2
