CPhill is working on this...I know he does this differently than what I am going to show ya....
Definition of parabola is the set of points that are equidistant from a point called the focus and a line called the directrix.
This parabola has the focus BELOW the directrix, so it opens downward....it looks like a dome.
Point x,y on the parabola has the same distance to the focus and the line y= 13
Distance to the focus is (x-5)^2 +(y-2)^2 = d^2
Distance to the directrix is simply d = 13-y d^2 = (13-y)^2 these two d^2 are equal
so
(x-5)^2 + (y-2)^2 = (13-y)^2 Expand and simplify to find your parabola equation
x^2 - 10x + 25 + y^2 - 4y + = y^2 -26y + 169 gather like terms and simplify and you will get
y = -1/22 x^2 + 10/22 x + 140/22 for your parabola
...here is a graph..... Well...you can look at CPHill's graph ! 
