$$\begin{gathered} \mathrm{Given} \mathrm{e}=\raisebox{1ex}{$\sqrt{3}$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ Now {\mathrm{b}}^2={\mathrm{a}}^2(1-{\mathrm{e}}^2) \\ ={\mathrm{a}}^2(1-\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.) \\ \Rightarrow b^{2_{ }}=\frac{{\mathrm{a}}^2}{4} \\ \Rightarrow \mathrm{b}=\raisebox{1ex}{$\mathrm{a}$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ Now \mathrm{L}.\mathrm{L}.\mathrm{R}=\frac{2{\mathrm{b}}^2}{\mathrm{a}} \\ =\frac{2\times {\displaystyle \raisebox{1ex}{${\mathrm{a}}^2$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}{\mathrm{a}} \\ =\frac{1}{2}\left(\mathrm{a}\right) \\ =\frac{1}{4}\left(2\mathrm{a}\right) \\ =\frac{1}{4}(\mathrm{Length} \mathrm{of} \mathrm{major} \mathrm{axis}) \end{gathered}$$