Q57.Let x2 a2 + b2 = 1(a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function, ϕ(t) = 125 + t −t2 , then a2 + b2 is equal to : (1) 145 (2) 116 (3) 126 (4) 135
What This Question Tests
This question requires using the properties of an ellipse (latus rectum and eccentricity) and finding the maximum value of a quadratic function to determine the eccentricity and subsequently the values of a² and b².
Concepts Tested
Formulas Used
Length of latus rectum = 2b²/a
b² = a²(1 - e²)
Eccentricity e = sqrt(1 - b²/a²)
Vertex of parabola for max/min: -b/(2a)
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📋 Question Details
- Chapter
- Ellipses
- Topic
- Properties of an ellipse
- Year
- 2020
- Shift
- 04 Sep Shift 1
- Q Number
- Q57
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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