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JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and the straight line \[y=mx+c\] intersect in real points only if         [MNR 1995]

    A)            \[{{a}^{2}}{{m}^{2}}<{{c}^{2}}-{{b}^{2}}\]                                   

    B)            \[{{a}^{2}}{{m}^{2}}>{{c}^{2}}-{{b}^{2}}\]

    C)            \[{{a}^{2}}{{m}^{2}}\ge {{c}^{2}}-{{b}^{2}}\]                               

    D)            \[c\ge b\]

    Correct Answer: C

    Solution :

               To cut at real points, \[{{c}^{2}}\le {{a}^{2}}{{m}^{2}}+{{b}^{2}}\]Þ \[{{a}^{2}}{{m}^{2}}\ge {{c}^{2}}-{{b}^{2}}\].


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