Define the collections $\left\{\mathrm{E}_1, \mathrm{E}_2, \mathrm{E}_3, \ldots ..\right\}$ of ellipses and $\left\{\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_3, \ldots ..\right\}$ of rectangles as follows :
$$
\mathrm{E}_1: \frac{\mathrm{x}^2}{9}+\frac{\mathrm{y}^2}{4}=1 ;
$$
$R_1$ : rectangle of largest area, with sides parallel to the axes, inscribed in $E_1$;
$E_n$ : ellipse $\frac{x^2}{a_n^2}+\frac{y^2}{b_n^2}=1$ of largest area inscribed in $R_{n-1}, n>1$;
$R_n$ : rectangle of largest area, with sides parallel to the axes, inscribed in $E_n, n>1$.
Then which of the following options is/are correct?
Select ALL correct options:
A
The eccentricities of $\mathrm{E}_{18}$ and $\mathrm{E}_{19}$ are NOT equal
B
The distance of a focus from the centre in $\mathrm{E}_9$ is $\frac{\sqrt{5}}{32}$
C
The length of latus rectum of $E_9$ is $\frac{1}{6}$
D
$\sum_{n=1}^N\left(\right.$ area of $\left.R_n\right)<24$, for each positive integer $N$
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