Question 936457
<pre>
First we have to graph the parabola:

[Always draw graphs when doing conic section problems].

{{{(y - 3)^2 = 8(x - 5)}}}

Compare it to 

{{{(y - k)^2 = 4a(x - h)}}}

So the vertex is (h,k) = (5,3).

It opens to the right because 4a=8 or a=2 is positive.

So we sketch in the parabola with vertex (5,3).

{{{drawing(400,400,-2,10,-2,8,
red(arc(6.045,3,2.3,-2.3,160,200)),
graph(400,400,-2,10,-2,8,3+sqrt(8(x-5)) ),

locate(3.7,3.2,"(5,3)"),

circle(5,3,0.15),circle(5,3,0.13),circle(5,3,0.11),circle(5,3,0.09),circle(5,3,0.07),circle(5,3,0.05),circle(5,3,0.03),circle(5,3,0.01),

graph(400,400,-2,10,-2,8,3-sqrt(8(x-5))) ) }}}

|a|=2 is the distance from both the vertex to both the focus and the directrix.
The focus is a point inside the parabola and the directrix is a line
outside the parabola line, which are the green point and line drawn below:

{{{drawing(400,400,-2,10,-2,8,
red(arc(6.045,3,2.3,-2.3,160,200)),
graph(400,400,-2,10,-2,8,3+sqrt(8(x-5)) ),

locate(3.7,3.2,"(5,3)"),
green(locate(7.3,3.2,"(7,3)")),
circle(5,3,0.15),circle(5,3,0.13),circle(5,3,0.11),circle(5,3,0.09),circle(5,3,0.07),circle(5,3,0.05),circle(5,3,0.03),circle(5,3,0.01),
green(locate(2,3.2,x=3)),

green(circle(7,3,0.15),circle(7,3,0.13),circle(7,3,0.11),circle(7,3,0.09),circle(7,3,0.07),circle(7,3,0.05),circle(7,3,0.03),circle(7,3,0.01),line(3,-20,3,20)),



graph(400,400,-2,10,-2,8,3-sqrt(8(x-5))) ) }}}

So as we see from the graph, the focus is (7,3) and the directrix is x=3.

I went ahead and found the focus because in other problems you will have
to find the focus.

Edwin</pre>