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Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3, .....} of rectangles as follows: 
R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1 ;
En: ellipse  of largest area inscribed in 
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?
  • a)
    The eccentricities of E18 and E19 are NOT equal
  • b)
    The distance of a focus from the centre in E9 is √5/32
  • c)
    The length of latus rectum of E9 is 1/6
  • d)
     for each positive integer N
Correct answer is option 'C,D'. Can you explain this answer?
Verified Answer
Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3...

Area of R1 = 3sin2θ ; for this to be maximum

Hence for subsequent areas of rectangles Rn to be maximum the coordinates will be in GP with common ratio 
Eccentricity of all the ellipses will be same
Distance of a focus from the centre in 
Length of latus rectum of 
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Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3, .....} of rectangles as follows:R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1 ;En: ellipseof largest area inscribed inRn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.Then which of the following options is/are correct?a)The eccentricities of E18 and E19 are NOT equalb)The distance of a focus from the centre in E9 is√5/32c)The length of latus rectum of E9 is 1/6d)for each positive integer NCorrect answer is option 'C,D'. Can you explain this answer?
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Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3, .....} of rectangles as follows:R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1 ;En: ellipseof largest area inscribed inRn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.Then which of the following options is/are correct?a)The eccentricities of E18 and E19 are NOT equalb)The distance of a focus from the centre in E9 is√5/32c)The length of latus rectum of E9 is 1/6d)for each positive integer NCorrect answer is option 'C,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3, .....} of rectangles as follows:R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1 ;En: ellipseof largest area inscribed inRn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.Then which of the following options is/are correct?a)The eccentricities of E18 and E19 are NOT equalb)The distance of a focus from the centre in E9 is√5/32c)The length of latus rectum of E9 is 1/6d)for each positive integer NCorrect answer is option 'C,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Define the collections {E1, E2, E3, .....} of ellipses and {R1, R2, R3, .....} of rectangles as follows:R1: rectangle of largest area, with sides parallel to the axes, inscribed in E1 ;En: ellipseof largest area inscribed inRn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1.Then which of the following options is/are correct?a)The eccentricities of E18 and E19 are NOT equalb)The distance of a focus from the centre in E9 is√5/32c)The length of latus rectum of E9 is 1/6d)for each positive integer NCorrect answer is option 'C,D'. Can you explain this answer?.
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