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Manipal Engineering Manipal Engineering Solved Paper-2013

  • question_answer
    Which one of the following is independent of a in the hyperbola\[(0<\alpha <\pi /2)\]\[\frac{{{x}^{2}}}{{{\cos }^{2}}\alpha }-\frac{{{y}^{2}}}{{{\sin }^{2}}\alpha }=1\]

    A)  Eccentricity                       

    B)  Abscissa of foci

    C)  Directrix              

    D)         Vertex

    Correct Answer: B

    Solution :

    \[{{e}^{2}}=1+\frac{{{b}^{2}}}{a2}=1+\frac{{{\sin }^{2}}\alpha }{{{\cos }^{2}}\alpha }=\frac{1}{{{\cos }^{2}}\alpha }\] and        \[{{a}^{2}}={{\cos }^{2}}\alpha \] \[\therefore \]\[{{a}^{2}}{{e}^{2}}=1\] \[\therefore \]\[foci(\pm ae,\,\,0)=(\pm 1,\,\,0)\], which Is independent of\[\alpha \].


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