Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $4x^{2} + 9y^{2} = 36$.

(A) The given equation is $4x^{2} + 9y^{2} = 36$.
Dividing both sides by $36$,we get:
$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
$\frac{x^{2}}{3^{2}} + \frac{y^{2}}{2^{2}} = 1$
Comparing this with the standard equation $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$,where $a > b$,we have $a = 3$ and $b = 2$.
The eccentricity $e$ is given by $e = \sqrt{1 - \frac{b^{2}}{a^{2}}} = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}$.
The foci are $(\pm ae, 0) = (\pm 3 \times \frac{\sqrt{5}}{3}, 0) = (\pm \sqrt{5}, 0)$.
The vertices are $(\pm a, 0) = (\pm 3, 0)$.
The length of the major axis is $2a = 2 \times 3 = 6$.
The length of the minor axis is $2b = 2 \times 2 = 4$.
The length of the latus rectum is $\frac{2b^{2}}{a} = \frac{2 \times 4}{3} = \frac{8}{3}$.