Thank you for reporting, we will resolve it shortly
Q.
Let $P ( h , k )$ be a point on the curve $y = x ^{2}+7 x +2$,
nearest to the line, $y =3 x -3 .$ Then the equation of the normal to the curve at $P$ is
Let $L$ be the common normal to parabola
$y=x^{2}+7 x+2$ and line $y=3 x-3$
$\Rightarrow $ slope of tangent of $y=x^{2}+7 x+2$ at $P=3$
$\left.\Rightarrow \frac{ dy }{ dx }\right]_{ For P }=3$
$\Rightarrow 2 x+7=3 \Rightarrow x=-2 \Rightarrow y=-8$
So $P (-2,-8)$
Normal at $P: x+3 y+C=0$
$\Rightarrow C =26$ (P satisfies the line)
Normal: $x+3 y+26=0$
