Hyperbola
The eccentricity of a hyperbola is always
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- hyperbola
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Greater than 1
- Relationship: For a hyperbola a2x2−b2y2=1, the semi-minor and semi-major axes relate to eccentricity as b2=a2(e2−1).
- Constraint Analysis: Since b2 and a2 are both positive, e2−1 must be positive.
- Result: e2>1⟹∗∗e>1∗∗.
- This reflects that the distance from the center to a focus (ae) is greater than the distance to the vertex (a).
This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of hyperbola. It appeared in the 2025 exam.
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