Problem Statement:-
Let $y=3x-8$ be the equation of tangent at the point $(7,13)$ lying on the parabola whose focus is at $(-1,-1)$. If the latus rectum of parabola is $k$ then find the value of $\lfloor{k^2}\rfloor$.
I could not think of much on this, but I did the find that the image of focus of the parabola w.r.t any tangent lies on the directrix by messing around in geogebra. Some hints to this problem would be great.