Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola. Suppose {P} is a parabola with focus (4,3) and directrix y=1. The point (8,6) is on {P} because (8,6) is 5 units away from both the focus and the directrix.

If we write the equation whose graph is {P} in the form $y=ax^2 + bx + c, then what is a+b+c?