the difference of the slopes of the lines 3x²-4xy+y²=0 is?
 

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{For} {\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0 \\ {\mathrm{m}}_1+{\mathrm{m}}_2=-\frac{2\mathrm{h}}{\mathrm{b}} \\ {\mathrm{m}}_1{\mathrm{m}}_2=\frac{\mathrm{a}}{\mathrm{b}} \\ \mathrm{We} \mathrm{have} \\ 3{\mathrm{x}}^2-4\mathrm{xy}+{\mathrm{y}}^2=0 \\ {\mathrm{m}}_1+{\mathrm{m}}_2=-\frac{-4}{1}=4 \\ {\mathrm{m}}_1{\mathrm{m}}_2=\frac{3}{1}=3 \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \left|{\mathrm{m}}_1-{\mathrm{m}}_2\right|=\sqrt{{\left({\mathrm{m}}_1+{\mathrm{m}}_2\right)}^2-4{\mathrm{m}}_1{\mathrm{m}}_2}=\sqrt{4^2-4\times 3}=\sqrt{4} \\ \Rightarrow \left|{\mathbf{m}}_{\mathbf{1}}\mathbf{-}{\mathbf{m}}_{\mathbf{2}}\right|\mathbf{=}\mathbf{2}\mathbf{ }\left[\mathbf{Answer}\right] \end{gathered}$$

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