$\text{ The equation }(5x-1{)}^2+(5y-2{)}^2=\left({\lambda }^2-4\lambda +4\right)(3x+4y-1{)}^2$$\text{ represents an ellipse if }\lambda \in$

$\begin{array}{l}{\left(x-\frac{1}{5}\right)}^2+{\left(y-\frac{2}{5}\right)}^2=\left({\lambda }^2-4\lambda +4\right){\left(\frac{3x+4y-1}{5}\right)}^2\\ \sqrt{{\left(x-\frac{1}{5}\right)}^2+{\left(y-\frac{2}{5}\right)}^2}=|\lambda -2|\left|\frac{3x+4y-1}{\sqrt{5}}\right|\text{\hspace{0.17em}is an ellipse}\\ \text{ if }0<|\lambda -2|<1\\ \Rightarrow -1<\lambda -2<1 and \lambda -2\ne 0\\ \Rightarrow 1<\lambda <3 and \lambda \ne 2.\\ \Rightarrow \lambda \in \left(1,2\right)\cup \left(2,3\right)\end{array}$