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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        The radius of the circle passing through the foci of the ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\]and having its centre at (0, 3) is:

    A)  4                                            

    B)  3

    C)  \[\sqrt{12}\]                                     

    D)  \[\frac{7}{2}\]

    Correct Answer: A

    Solution :

                    We have \[{{a}^{2}}=16\] and     \[9{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\]                 \[9=16(1-{{e}^{2}})\] So,          \[e=\frac{\sqrt{7}}{4}\] Thus, the foci are\[(\pm \sqrt{7},0)\] The radius of required circle                 \[=\sqrt{{{(\sqrt{7}-0)}^{2}}+{{3}^{2}}}\]                 \[=\sqrt{7+9}\]                 \[=4\]


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