The points of contact of the tangents drawn from the point (4, 6) to the parabola ${\mathrm{y}}^2=8\mathrm{x}$
 

$$\begin{gathered} Given parabola S\equiv y^2-8x \\ Given point \left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=\left(4, 6\right) \\ \mathrm{Eq}uation \mathrm{of} chord of contact is {\mathrm{S}}_1=0 \end{gathered}$$

$$\begin{gathered} \mathrm{y} {\mathrm{y}}_1-4\left(\mathrm{x}+{\mathrm{x}}_1\right)=0 \\ \Rightarrow 6\mathrm{y}-16=4x\to \left(2\right) \\ From \left(1\right) \\ {y}^2=2(6\mathrm{y}-16) \\ \Rightarrow y^2-12y+32=0 \\ \Rightarrow (y-4)(y-8)=0 \\ \Rightarrow y=4 or y=8 \\ from \left(2\right) \\ If y=4 then x=2 \\ If y=8 then x=8 \\ Required points are (2, 4) (8, 8) \end{gathered}$$