Find the equation of the normal to the parabola ${\mathrm{y}}^2=4\mathrm{x}$ which is parallel to y - 2x + 5 = 0

Equation of the parabola is y² = 4x
$\Rightarrow \mathrm{a}=1$
The equation of the given line y - 2x + 5 = 0
Slope m = 2
Since normal is parallel to the line y - 2x + 5 = 0 then
Slope of the normal = 2
Now equation of the normal at ‘t’ is
 $\begin{array}{l}\mathrm{y}+\mathrm{tx}=2\mathrm{at}+{\mathrm{at}}^3\\ \therefore \text{ Slope }=-\mathrm{t}=2\Rightarrow \mathrm{t}=-2\end{array}$
Equation of the normal is
$\begin{array}{l}\mathrm{y}-2\mathrm{x}=2.1(-2)+1(-2{)}^3\\ =-4-8=-12\\ 2\mathrm{x}-\mathrm{y}-12=0\end{array}$