prove that every homogeneous equation of degree two in x and y represents pair of lines through the origin

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$$\begin{gathered} \mathrm{General} \mathrm{homogenous} \mathrm{equation} \mathrm{of} \mathrm{second} \mathrm{degree}: \\ {\mathrm{ax}}^2+2\mathrm{hxy}+{\mathrm{by}}^2=0 ---\left(1\right) \\ \mathrm{This} \mathrm{can} \mathrm{be} \mathrm{written} \mathrm{as}: \\ {\left(\mathrm{ax}+\mathrm{hy}\right)}^2-\left({\mathrm{h}}^2-\mathrm{ab}\right){\mathrm{y}}^2=0 \\ \left\{\mathrm{ax}+\left(\mathrm{h}+\sqrt{{\mathrm{h}}^2-\mathrm{ab}}\right)\mathrm{y}\right\}\left\{\mathrm{ax}+\left(\mathrm{h}-\sqrt{{\mathrm{h}}^2-\mathrm{ab}}\right)\mathrm{y}\right\}=0 \\ \mathrm{so} \mathrm{equation} 1 \mathrm{represents}: \\ \mathrm{ax}+\left(\mathrm{h}+\sqrt{{\mathrm{h}}^2-\mathrm{ab}}\right)\mathrm{y}=0 \\ \mathrm{ax}+\left(\mathrm{h}-\sqrt{{\mathrm{h}}^2-\mathrm{ab}}\right)\mathrm{y}=0 \\ \mathbf{which}\mathbf{ }\mathbf{represents}\mathbf{ }\mathbf{,}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{pair}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{lines}\mathbf{ }\mathbf{through}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{origin}\mathbf{.}\mathbf{ } \end{gathered}$$

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