Normal Line Equation to the curves at the given point of tangency

$\mathit{y}\mathbf{=}\mathbf{(}{\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathbf{1}{\mathbf{)}}^{\mathbf{2}}\mathbf{ }\mathbf{a}\mathbf{t}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{ }\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{9}\mathbf{)}\mathbf{ }$

$\mathbf{S}\mathbf{t}\mathbf{e}\mathbf{p} 1: \mathbf{G}\mathbf{e}\mathbf{t}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{D}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{v}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{v}\mathbf{e}\mathbf{ }\mathbf{b}\mathbf{y}\mathbf{ }\mathbf{A}\mathbf{p}\mathbf{p}\mathbf{l}\mathbf{y}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{G}\mathbf{e}\mathbf{n}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{l} \mathbf{P}\mathbf{o}\mathbf{w}\mathbf{e}\mathbf{r}\mathbf{ }\mathbf{R}\mathbf{u}\mathbf{l}\mathbf{e}$

$$\begin{gathered} \text{ \\ ddx(cun)=cnun-1dudx} \end{gathered}$$

$$\begin{gathered} \text{ \\ dydx=2x2-12-12x} \end{gathered}$$

$$\begin{gathered} \text{ \\ dydx=4xx2-1 \\ } \end{gathered}$$

$\mathbf{S}\mathbf{t}\mathbf{e}\mathbf{p}\mathbf{ }\mathbf{2}\mathbf{:}\mathbf{ }\mathbf{G}\mathbf{e}\mathbf{t}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{s}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{ }\mathbf{a}\mathbf{t}\mathbf{ }\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{ }\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{9}\mathbf{)}$

$$\begin{gathered} \text{ \\ m=4(-2)-22-1} \end{gathered}$$

$$\begin{gathered} \text{ \\ m=-8(3)} \end{gathered}$$

$$\begin{gathered} \text{ \\ m=-24 \\ } \end{gathered}$$

$\mathbf{S}\mathbf{t}\mathbf{e}\mathbf{p}\mathbf{ }\mathbf{3}\mathbf{:}\mathbf{ }\mathbf{A}\mathbf{p}\mathbf{p}\mathbf{l}\mathbf{y}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{E}\mathbf{q}\mathbf{u}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{N}\mathbf{o}\mathbf{r}\mathbf{m}\mathbf{a}\mathbf{l}\mathbf{ }\mathbf{L}\mathbf{i}\mathbf{n}\mathbf{e}\mathbf{ }\mathbf{a}\mathbf{t}\mathbf{ }\mathbf{p}\mathbf{o}\mathbf{i}\mathbf{n}\mathbf{t}\mathbf{ }\mathbf{(}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{ }\mathbf{9}\mathbf{)}$

$$\begin{gathered} \text{ \\ y-y1=-1m(x-x1)} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-9=--124(x--2)} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-9=124(x+2)24} \end{gathered}$$

$$\begin{gathered} \text{ \\ 24} \end{gathered}$$y-216=x+2

24y-216-x-2=0

$$\begin{gathered} \text{ \\ x-24y+218=0 \\ } \end{gathered}$$

$\mathbf{F}\mathbf{i}\mathbf{n}\mathbf{a}\mathbf{l}\mathbf{ }\mathbf{A}\mathbf{n}\mathbf{s}\mathbf{w}\mathbf{e}\mathbf{r}\mathbf{:}\mathbf{ }\mathit{x}\mathbf{-}\mathbf{24}\mathit{y}\mathbf{+}\mathbf{218}\mathbf{=}\mathbf{0}$