Troublesome parabola

Let $s=0$ be a parabola touching the $x$ -axis at $(1,0)$ and $y=x$ at $(1,1)$ , respetively. Let $(a,b)$ and $(p,q)$ be the focus and the vertex of the parabola.

The slope of the axis of the parabola can be expressed as $\dfrac mn$ , where $m$ and $n$ are coprime positive integers.

The equation of the directrix is $dx + fy -e = 0$ , where $d,e,f$ are coprime positive integers.

If $\dfrac{p-q}{a^2}= k$ , find the value of $m+n+k+d+e+f$ .