Q96.For the hyperbola = 1 , which of the following remains constant when α varies? cos2 α α − sin2 (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci
What This Question Tests
This question requires knowledge of the standard form of a hyperbola and its key properties (eccentricity, vertices, foci, directrices). It tests the ability to derive expressions for these properties in terms of the given parameter and identify which one remains constant.
Concepts Tested
Formulas Used
Equation of hyperbola y^2/b^2 - x^2/a^2 = 1
Relation between a, b, e: b^2 = a^2(e^2-1)
Coordinates of vertices: (0, +/-b)
Coordinates of foci: (0, +/-be)
Equations of directrices: y = +/-b/e
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📋 Question Details
- Chapter
- Hyperbola
- Topic
- Standard Equation of Hyperbola, Eccentricity, Foci, Vertices, Directrix
- Year
- 2007
- Shift
- Unknown
- Q Number
- Q96
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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