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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    The eccentricity of the conjugate hyperbola of hyperbola \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3}{{\mathbf{y}}^{\mathbf{2}}}=\mathbf{1}\]is

    A)  1                                

    B)  2            

    C)  3                                

    D)  4

    Correct Answer: B

    Solution :

    [b] Conjugate hyperbola of hyperbola \[{{x}^{2}}-3{{y}^{2}}=1\text{ }be\text{ }3{{x}^{2}}-{{y}^{2}}=1\] Now, \[e=a.\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{3+1}=\sqrt{4}=2\].


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