Define the collections \( \left\{E_{1}, E_{2}, E_{3}, \ldots \ldots\right\} \) of ellipes and \( \left\{R_{1}, R_{2}, R_{3}, \ldots ..\right\} \) of rectangles as follows :
\( \mathrm{P} \)
\[
E_{1}: \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 \text {; }
\]
W
\( R_{1} \) : rectangle of largest area, with sides parallel to the axes, inscribed in \( E_{1} \); [JEE Advanced-2019]
\( E_{n}: \) ellipse \( \frac{x^{2}}{a_{n}^{2}}+\frac{y^{2}}{b_{n}^{2}}=1 \) of largest area inscribed in \( R_{n-1}, n1 \);
\( R_{n} \) : rectangle of largest area, with sides parallel to the axes, inscribed in \( E_{n}, n1 \).
Then which of the following options is/are correct ?
(a) The eccentricities of \( E_{18} \) and \( E_{19} \) are NOT equal
(b) The distance of a focus from the centre in \( E \), is \( \frac{\sqrt{5}}{32} \)
(c) The length of latus rectum of \( E_{9} \) is \( \frac{1}{6} \)
(d) \( \sum_{n=1}^{N} \) (area of \( R_{n} \) ) \( 24 \), for each positive integer \( N \)
š²PW App Link - https://bit.ly/YTAI_PWAP
šPW Website - https://www.pw.live
0