$\mathrm{y}=3\mathrm{x}-2$ is a straight line touching the parabola ${\left(\mathrm{y}-3\right)}^2=12\left(\mathrm{x}-2\right)$. If a line drawn perpen-dicular to this line at P on it, touches the given parabola, then the point P is

From the given data P lies on directrix of parabola

$$\begin{gathered} Given parabola {(\mathrm{y}-3)}^2=12(\mathrm{x}-2) \\ \Rightarrow 4a=12\Rightarrow a=3 \\ Equation of directri is \mathrm{x}-2+3=0 \\ \mathrm{x}=-1 \\ sub x=-1 in line y=3x-2 \\ \Rightarrow \mathrm{y}=-3-2=-5 \\ Required point =\mathrm{P}(-1, -5) \end{gathered}$$