Let $A(4,-2)$ and $B(0,1)$ be two points on the parabola, normals at which intersect at the point P(2,2) then equation of directrix is $y+k=0$ and focus of parabola is $(\frac{16}{l},\frac{-7}{l})$.then $k+l$ is_____

The normal’s are perpendicular, Equation of tangents at A,B are respectively $x-2y=8,2x+y=1$. Point of intersection is $p(2,-3)$. It lies on directrix.
Midpoint of  $\overline{AB}=(2,-\frac{1}{2})=C$
$$\begin{gathered} \overline{PC}\text{ slope is undefined} \\ \overline{PC}\text{ is parallel to axis} \\ \Rightarrow axis\text{ slope is undefined} \\ \Rightarrow \text{directrix slope is O} \\ \Rightarrow \text{ equation of directrix is y = -3} \end{gathered}$$

Foot of A on directrix is (4, -3) Image of (4, -3 ) w.r.t tangent at A i.e, $x-2y-8=0$ is the focus $(\frac{16}{5},\frac{-7}{5})$