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JEE Main & Advanced Mathematics Conic Sections Question Bank Mock Test - Conic Sections

  • question_answer
    The liner \[x={{t}^{2}}\]meets the ellipse \[{{x}^{2}}+\frac{{{y}^{2}}}{9}=1\]at real and distinct points if and only if

    A) \[\left| t \right|<2\]    

    B) \[\left| t \right|<1\]

    C) \[\left| t \right|>1\]    

    D) None of these

    Correct Answer: C

    Solution :

    [b] solving the given line and the ellipse, we get \[{{r}^{2}}+\frac{{{y}^{2}}}{9}=1\] Or \[{{y}^{2}}=9(1-{{r}^{2}})\] Which gives the real and distinct values of y if \[1-{{r}^{2}}>0\] Or \[t\in (-1,1)\]


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