Define the collections \{E_1,E_2,E_3,......\} of ellipses and \{R_1,R_2,R_3,......\} of rectangles as follows:E_{1}: \frac{x^{2}}{9}+ \frac{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 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? [JEE Adv 2019 P1]

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

The length of latus rectum of E_9 is 1/6

The eccentricities of E_18 and E_19 are NOT equal

\sum_{n=1}^{N}(\text{area of} R_n) < 24 for each positive integer N

Ellipse

Section: Mathematics

Question : 6 of 25

Marks: +1, -0

Define the collections {E1,E2,E3,......} of ellipses and {R1,R2,R3,......} of rectangles as follows:E1:‌‌

+‌‌

=1
R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1;
En ellipse ‌‌

an2

+‌‌

bn2

=1 of largest area inscribed in Rn−1,n>1
Rn: rectangle of largest area, with sides parallel to the axes, inscribed in En,n>1
Then which of the following options is/are correct?

[JEE Adv 2019 P1]

The distance of a focus from the centre in E9 is
√5
32
The length of latus rectum of E9 is
1
6
The eccentricities of E18 and E19 are NOT equal
N
∑
n=1
(area of‌Rn)<24 for each positive integer N

Validate

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