$\begin{aligned} & \text y=m x+4 \\ & \Rightarrow \frac{x^2}{25}-\frac{y^2}{9}=1 \\ & \because c^2=a^2 m^2-b^2 \Rightarrow 16=25 m^2-9 \\ & \Rightarrow m^2=1 \Rightarrow m=1 \\ & \therefore \text { Point of contact }\left(\frac{-a^2 m}{\sqrt{a^2 m^2-b^2}}, \frac{-b^2}{\sqrt{a^2 m^2-b^2}}\right) \\ & =\left(\frac{-25}{\sqrt{25-9}}, \frac{-9}{\sqrt{25-9}}\right)=\left(\frac{-25}{4}, \frac{-9}{4}\right) .\end{aligned}$