Point of intersection of tangents to the parabola ${(\mathrm{y}-2)}^2=4(\mathrm{x}-1)$ at the ends of latus rectum is 
 

$$\begin{gathered} {\left(\mathrm{y}-2\right)}^2=4\left(\mathrm{x}-1\right) \\ \Rightarrow 4\mathrm{a}=4 \\ \Rightarrow \mathrm{a}=1 \\ \mathrm{Vertex}=\left(1,2\right) \\ focus \mathrm{S}=\left(\mathrm{a}+\mathrm{h},\mathrm{k}\right) \\ \Rightarrow \mathrm{S}=\left(2,2\right) \\ point of intersection of \tan gents at extremities of latusrectum of parabola \\ is foot of directrix \\ Now equation of directrix is x-h+a=0 \\ \Rightarrow x-1+1=0 \\ \Rightarrow x=0 \\ Now foot of perpendicular from (2,2) to x=0 is (0,2) \end{gathered}$$