Q86.Let the hyperbola H : x2 −y2 = 1 and the ellipse E : 3x2 + 4y2 = 12 be such that the length of latus rectum a2 of H is equal to the length of latus rectum of E . If eH and eE are the eccentricities of H and E respectively, then the value of 12(e2H + e2E) is equal to _____.
What This Question Tests
This question tests the ability to extract parameters (a, b) from the equations of a hyperbola and an ellipse, then calculate their respective latus rectum lengths and eccentricities to satisfy the given conditions.
Concepts Tested
Formulas Used
Latus Rectum of Hyperbola = 2b^2/a
Latus Rectum of Ellipse = 2b^2/a
eH^2 = 1 + b^2/a^2
eE^2 = 1 - b^2/a^2
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📋 Question Details
- Chapter
- Hyperbola
- Topic
- Latus rectum and eccentricity of hyperbola and ellipse
- Year
- 2022
- Shift
- 24 Jun Shift 2
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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