The distance from any point P (x,y) on the parabola to the focus = the distance of this point from the directrix.
distance between P to focus:-
= sqrt ( x - 2)^2 + (y - 5))^2
distance from the point to directrix = ( 9 - y)
so sqrt( x - 2)^2 + (y-5)^2 = 9 -y
(x - 2)^2+ (y - 5)^2 = (9-y)^2
x^2 -4x + 4 + y^2 - 10y + 25 = 81 - 18y + y^2
x^2 - 4x + 4 +25 - 81 = -18y + 10y
-8y = x^2 - 4x -52
y = (-1/8)^2 + 1/2 x + 6 1/2 is the required equation
