WBJEE · Maths · Hyperbola
For the hyperbola \(\frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1,\) which of the following remains fixed when \(\alpha\) varies?
- A directrix
- B vertices
- C foci
- D eccentricity
Answer & Solution
Correct Answer
(C) foci
Step-by-step Solution
Detailed explanation
Given, equation of hyperbola is \[ \frac{x^{2}}{\cos ^{2} \alpha}-\frac{y^{2}}{\sin ^{2} \alpha}=1 \] Here, \(a^{2}=\cos ^{2} \alpha\) and \(b^{2}=\sin ^{2} \alpha\) [i.e. comparing with standard \[ \text { equation } \left.\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\right] \] We…
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