Function Parabola Tangent Normal

Let the function f(x)=2x2−logex,x>0, be decreasing in (0,a) and increasing in (a,4). A tangent to the parabola y2=4ax at a point P on it passes through the point (8a,8a−1) but does not pass through the point (−‌

1

a

,0). If the equation of the normal at P is : ‌

x

α

+‌

y

β

=1, then α+β is equal to _________.