Pls answer q20

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{In} \mathrm{pairs} \mathrm{of} \mathrm{lines} \\ {\mathrm{Ax}}^2+2\mathrm{Hxy}+{\mathrm{By}}^2=0 \\ \mathrm{Lines} \mathrm{are} \mathrm{perpendicular} \mathrm{if} \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{x}}^2+\mathrm{Coefficient} \mathrm{of} {\mathrm{y}}^2=0 \\ \mathrm{We} \mathrm{have} \\ {\mathrm{ax}}^2+\left(1+\mathrm{\lambda }\right)\mathrm{xy}-{\mathrm{ay}}^2=0 \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{x}}^2=\mathrm{a} \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{y}}^2=-\mathrm{a} \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{x}}^2+\mathrm{Coefficient} \mathrm{of} {\mathrm{y}}^2 \\ =\mathrm{a}-\mathrm{a}=0 \\ \mathrm{Hence} \mathrm{angle} \mathrm{between} \mathrm{lines} \mathrm{is} 90° \\ \mathrm{In} \mathrm{xy}=0 \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{x}}^2=0 \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{y}}^2=0 \\ \mathrm{Coefficient} \mathrm{of} {\mathrm{x}}^2+\mathrm{Coefficient} \mathrm{of} {\mathrm{y}}^2 \\ =0+0=0 \\ \mathrm{Hence} \mathrm{angle} \mathrm{between} \mathrm{lines} \mathrm{is} 90° \\ \mathrm{Hence} \mathrm{option}\left(\mathrm{C}\right) \mathrm{is} \mathrm{correct}. \end{gathered}$$

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