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Ellipse question

2019 · Shift 1 · Q24
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  2. /JEE Advanced
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  5. /2019 · Shift 1 · Q24

Ellipse question

2019 · Shift 1 · Q24

JEE AdvancedMathematicsEllipseMultiple correct+4 / −1
Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows : E1:x29+y24=1{E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1E1​:9x2​+4y2​=1 R1 : rectangle of largest area, with sides parallel to the axes, inscribed in E1; En : ellipse x2an2+y2bn2=1{{{x^2}} \over {a_n^2}} + {{{y^2}} \over {b_n^2}} = 1an2​x2​+bn2​y2​=1 of the largest area inscribed in Rn−1,n>1{R_{n - 1}},n \gt 1Rn−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?
  1. A
    The eccentricities of E18 and E19 are not equal.
  2. B
    The distance of a focus from the centre in E9 is 532{{\sqrt 5 } \over {32}}325​​.
  3. C
    ∑n=1N(area of Rn)\sum\limits_{n = 1}^N {(area\,of\,{R_n})}n=1∑N​(areaofRn​) < 24, for each positive integer N.
  4. D
    The length of latusrectum of E9 is 16{1 \over 6}61​
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