Equation of tangent to parabola ${\mathrm{y}}^2=16\mathrm{x}$ and perpendicular to the line x – 4y–7 = 0

$$\begin{gathered} {\mathrm{y}}^2=16\mathrm{x} \\ 4\mathrm{a}=16 \\ \mathrm{a}=4 \end{gathered}$$

Equation  of tangent is 

$$\begin{gathered} 4\mathrm{x}+\mathrm{y}+\mathrm{k}=0\to \left(1\right) \\ \mathrm{y}=-4\mathrm{x}-\mathrm{k} \\ \mathrm{since} \mathrm{it} \mathrm{is} \mathrm{tangent} \mathrm{then} \mathrm{c}=\frac{\mathrm{a}}{\mathrm{m}} \\ \Rightarrow -\mathrm{k}=\frac{4}{-4}=-1 \\ \Rightarrow \mathrm{k}=1 \\ from \left(1\right) 4\mathrm{x}+\mathrm{y}+1=0 \end{gathered}$$