The defining characteristic of a parabola is that any (x,y) point on it is exactly the same distance away from its focus point and the point on the directrix that forms a perpendicular line segment to the focus point.
The distance from the focus point (3,1) is √[(x-3)2 + (y-1)2].
And the perpendicular distance from (3,1) to the x=9 directrix line point (9,1) is just |x-9| since Δy = 0.
Hence, solve: √[(x-3)2 + (y-1)2] = |x-9| by squaring both sides, expanding, and combining like terms:
[(x-3)2 + (y-1)2] = (x-9)2 so (x2 - 6x +9) + (y2 - 2y + 1) = x2 -18x + 81 , the x2 terms cancel out, and
x = (-1/12) y2 + (1/6) y + (71/12)
That's the equation for this parabola. If you graph it, it opens up to the left, is symmetrical about the line y=+1 through the focus point, and goes thru (6, 1) where its distance is 3 from the focus and the directrix line.