Q68.Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola x2 −y2 = 1. Let e′ and l′ respectively the eccentricity and length of the latus rectum of its conjugate a2 b2 hyperbola. If e2 = 1411 l and (e′)2 = 118 l′ , then the value of 77a + 44b is equal to (1) 100 (2) 110 (3) 120 (4) 130
What This Question Tests
Tests the understanding of eccentricity and latus rectum formulas for a hyperbola and its conjugate, requiring algebraic manipulation to solve for parameters 'a' and 'b'.
Concepts Tested
Formulas Used
e^2 = 1 + b^2/a^2
l = 2b^2/a
(e')^2 = 1 + a^2/b^2
l' = 2a^2/b
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Hyperbola
- Topic
- Eccentricity and latus rectum of hyperbola
- Year
- 2022
- Shift
- 28 Jun Shift 2
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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