If the normals at the end points of a variable chord PQ of the parabola ${\mathrm{y}}^2-4\mathrm{y}-2\mathrm{x}=0$ are perpendicular, then the tangents at P and Q will intersect on

Point of intersection of  tangents lies on directrix

$$\begin{gathered} \mathrm{Given} \mathrm{parabola} {\mathrm{y}}^2-4\mathrm{y}=2x \\ {\Rightarrow (\mathrm{y}-2)}^2=2(x+2) \\ \Rightarrow 4a=2 \\ \Rightarrow a=\frac{1}{2} \\ Now equation of d\mathrm{irectrix} is x-h+a=0 \\ \Rightarrow \mathrm{x}+2+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=0 \\ \Rightarrow 2\mathrm{x}+5=0 \end{gathered}$$