Find the distance between the pair of parallel lines $9{\mathrm{x}}^2-6\mathrm{xy}+{\mathrm{y}}^2+18\mathrm{x}-6\mathrm{y}+8=0$

Given equation $9{\mathrm{x}}^2-6\mathrm{xy}+{\mathrm{y}}^2+18\mathrm{x}-6\mathrm{y}+8=0$ comparing with
$\begin{array}{l}{\mathrm{ax}}^2+2\mathrm{bxy}+{\mathrm{by}}^2+2\mathrm{gx}+2\mathrm{fy}+\mathrm{c}=0\\ \mathrm{a}=9;2\mathrm{h}=-6;\mathrm{b}=1;2\mathrm{g}=18;2\mathrm{f}=-6;\mathrm{c}=8\\ \mathrm{h}=-3;\mathrm{g}=9;\mathrm{f}=-3\end{array}$
Distance between the paralle lines
$\begin{array}{l}\mathrm{d}=2\sqrt{\frac{{\mathrm{g}}^2-\mathrm{ac}}{\mathrm{a}(\mathrm{a}+\mathrm{b})}}=2\sqrt{\frac{81-9\left(8\right)}{9(9+1)}}=2\sqrt{\frac{81-72}{9\left(10\right)}}\\ =2\sqrt{\frac{9}{9\left(10\right)}}=\frac{2}{\sqrt{10}}\\ =\frac{\sqrt{2}\cdot \sqrt{2}}{\sqrt{2}\sqrt{5}}\\ \mathrm{d}=\sqrt{\frac{2}{5}}\end{array}$