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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    Foci of the hyperbola \[\frac{{{x}^{2}}}{16}-\frac{{{(y-2)}^{2}}}{9}=1\] are

    A)            (5, 2) (?5, 2)                              

    B)            (5, 2) (5, ?2)

    C)            (5, 2) (?5, ?2)                            

    D)            None of these

    Correct Answer: A

    Solution :

                       \[a=4,\,b=3\] Þ \[\frac{9}{16}=({{e}^{2}}-1)\] Þ \[e=\frac{5}{4}\]                    Vertex is (0, 2). Hence focus is \[(\pm ae,\,2)=(\pm 5,\,2)\].


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