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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The equations of the directrices of the ellipse \[16{{x}^{2}}+25{{y}^{2}}=400\] are

    A)            \[2x=\pm 25\]                          

    B)            \[5x=\pm 9\]

    C)            \[3x=\pm 10\]                          

    D)            None of these

    Correct Answer: D

    Solution :

               \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] Þ \[e=\sqrt{1-\frac{16}{25}}=\frac{3}{5}\] Therefore, directrices are \[x\pm \frac{5}{3/5}=0\] or \[3x\pm 25=0\].


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