If a line $\frac{\mathrm{x}}{8}+\frac{\mathrm{y}}{5}=1$ meets the ellipse on x-axis and the line $\frac{\mathrm{x}}{3}+\frac{\mathrm{y}}{4}=1$ meets the ellipse on y-axis then its eccentricity

$$\begin{gathered} \frac{\mathrm{x}}{8}+\frac{\mathrm{y}}{5}=1 meets ellipse on x-axis then \\ \mathrm{put} \mathrm{y}=0\Rightarrow \mathrm{x}=8=\mathrm{a} \\ line \frac{\mathrm{x}}{3}+\frac{\mathrm{y}}{4}=1 \mathrm{meet}s ellipse on \mathrm{y}-\mathrm{axi}s then \\ put \mathrm{x}=0\Rightarrow \mathrm{y}=4=\mathrm{b} \\ Now \mathrm{e}=\sqrt{\frac{64-16}{64}}=\sqrt{\frac{48}{64}}=\frac{\sqrt{3}}{2} \end{gathered}$$