$$ \begin{aligned} & 4 x^3-3 x y^2+6 x^2-5 x y-8 y^2+9 x+14=0 \text { at } P(-2,3) \\\\ & 12 x^2-3\left(y^2+2 y x y^{\prime}\right)+12 x-5\left(x y^{\prime}+y\right)-16 y y^{\prime} + 9=0 \\\\ & 48-3\left(9-12 y^{\prime}\right)-24-5\left(-2 y^{\prime}+3\right)-48 y^{\prime}+9 =0 \\\\ & y^{\prime}=-9 / 2 \\\\ & \text { Tangent } y-3=-\frac{9}{2}(x+2) \Rightarrow 9 x+2 y=-12 \\\\ & \text { Normal : } y-3=\frac{2}{9}(x+2) \Rightarrow 9 y-2 x=31 \end{aligned} $$


$$ \begin{aligned} & \text { Area }=\frac{1}{2}\left(\frac{31}{2}-4\right) \times 3=\frac{85}{4} \\\\ & 8 \mathrm{~A}=170 \end{aligned} $$