the angle between pair of lines whose equation is 4xsquare +10 xy +m y square + 5x +10 y = 0 is answer shows tan inverse 3/8, is it correct if not what is its answer.

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$$\begin{gathered} 4{\mathrm{x}}^2+10\mathrm{xy}+{\mathrm{my}}^2+5\mathrm{x}+10\mathrm{y}=0 \\ \mathrm{On} \mathrm{comparing} \mathrm{it} \mathrm{with} \mathrm{standard} \mathrm{equation} {\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2+2\mathrm{gx}+2\mathrm{fy}+\mathrm{c}=0, \mathrm{we} \mathrm{get}, \\ \mathrm{a}=4, \mathrm{h}=5, \mathrm{b}=\mathrm{m}, \mathrm{g}=\frac{5}{2}, \mathrm{f}=5, \mathrm{c}=0 \\ \mathrm{For} \mathrm{pair} \mathrm{of} \mathrm{straight} \mathrm{lines}, \\ ∆=\mathrm{abc}+2\mathrm{fgh}-{\mathrm{af}}^2-{\mathrm{bg}}^2-{\mathrm{ch}}^2=0 \\ \Rightarrow 0+2\times 5\times \frac{5}{2}\times 5-4\times 25-\mathrm{m}\times \frac{25}{4}-0=0 \\ \Rightarrow 125-100=\frac{25\mathrm{m}}{4} \\ \Rightarrow \frac{25\mathrm{m}}{4}=25 \\ \Rightarrow \mathrm{m}=4 \\ \Rightarrow \mathrm{b}=4 \\ \mathrm{Angle} \mathrm{between} \mathrm{pair} \mathrm{of} \mathrm{straight} \mathrm{lines} =\mathrm{tan\theta }=\frac{2\sqrt{{\mathrm{h}}^2-\mathrm{ab}}}{\mathrm{a}+\mathrm{b}} \\ \Rightarrow \mathrm{tan\theta }=\frac{2\sqrt{25-4\times 4}}{4+4} \\ =\frac{2\sqrt{9}}{8} \\ \Rightarrow \mathrm{tan\theta }=\frac{3}{4} \\ \mathbf{\Rightarrow }\mathbf{\theta }\mathbf{=}{\mathbf{tan}}^{\mathbf{-}\mathbf{1}}\left(\frac{\mathbf{3}}{\mathbf{4}}\right)\mathbf{ }\mathbf{ }\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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