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Define the collection `{E_1,E_2,E_3,"....."}` of ellipses and `{R_1,R_2,R_3,"....."}` of rectangles as follows:
`E_1= (x^2)/(9)+(y^2)/(4)=1` ,
`R_1` : rectangle of largest area, with sides parallel to the axes, inscribed in `E_1` ,
`E_n` : ellipse `(x^2)/(a_(n)^(2))+(y^2)/(b_(n)^(2))=1` of largest are inscribed in `R_(n-1), n gt 1`.
then which of the following options is/are corrct?

A

The eccentricities of `E_(18) and E_(19)` are NOT equal

B

`sum_(n=1)^(N)` (area of `R_n` ) `lt` 24, for each positive integer N

C

The length of latus rectum of `E_9` is `1/6`

D

The distance of a focus from the centre in `E_9` is `sqrt5/32`

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