JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 29

Let the function $f(x)=2x^2-\log_ex$, $x>0$, be decreasing in $(0,a)$ and increasing in $(a,4)$. A tangent to the parabola $y^2=4ax$ at a point P on it passes through the point $(8a,8a-1)$ but does not pass through the point $\left(-\dfrac1a,0\right)$. If the equation of the normal at P is $\dfrac x\alpha+\dfrac y\beta=1$, then $\alpha+\beta$ is equal to ______.