Find the equation of ellipse whose eccentricity is $\large\frac{2}{3}$ , latus rectum is 5 and the centre is (0, 0).

Question

$\begin{array}{1 1}\large\frac{x^2}{81}+\frac{y^2}{45}\normalsize =1\\\large\frac{4x^2}{81}+\frac{4y^2}{45}\normalsize =1\\\large\frac{x^2}{81}-\frac{y^2}{45}\normalsize =1\\\large\frac{4x^2}{81}-\frac{4y^2}{45}\normalsize =1\end{array} $