If the length of the semi major axis of an ellipse is 68 and eccentricity is 1/2 then the area of the rectangle formed by joining the ends of the Latusrecta of the ellipse is equal to

$\mathrm{Given} \mathrm{a}=68 and \mathrm{e}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

$$\begin{gathered} A\mathrm{rea} of rec\tan gle=\frac{2{\mathrm{b}}^2}{\mathrm{a}}\times 2\mathrm{ae} \\ =4{\mathrm{b}}^2\mathrm{e} \\ =4\times {\mathrm{a}}^2(1-{\mathrm{e}}^2)\mathrm{e} \\ =4\times {\left(68\right)}^2 \times \left(1-\frac{1}{4}\right) \left(\frac{1}{2}\right) \\ =3\times 68\times 68\times \frac{1}{2} \\ =3\times 34\times 68 \\ =6936 \end{gathered}$$