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?
A similar question has been answered by CPhill here : https://web2.0calc.com/questions/the-graph-of-the-equation-y-ax-2-bx-c-where-a-b-and-c-are-constants-is-a-parabola-with-axis-of-symmetry-x-3-find-b-a
but his answer was incorrect.
