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  • Which of the following pairs may represent the eccentricities of two conjugate hyperbolas, for all <img alt="\alpha \in\left (0, \frac{\pi}{2} \right )" src="https://entrancecorner.oncodecogs.com/g

Which of the following pairs may represent the eccentricities of two conjugate hyperbolas, for all \alpha \in\left (0, \frac{\pi}{2} \right ) ?
 

Option: 1

\sin \theta, \cos \theta


Option: 2

\sec \theta, \operatorname{cosec} \theta


Option: 3

\tan \theta, \cot \theta


Option: 4

1+\sin \theta, 1+\cos \theta


Answers (1)

best_answer

 If \mathrm{e_1} and \mathrm{e_2} are the eccentricities of two conjugate hyperbolas, then \mathrm{ \frac{1}{c_1^2}+\frac{1}{e_2^2}=1}

\mathrm{Therefore, e_1=\sec \theta ~and ~e_2=\operatorname{cosec} \theta.}

Posted by

himanshu.meshram

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