JEE Main & Advanced Mathematics Conic Sections Question Bank Ellipse

  • question_answer
    The equation \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0\] represents an ellipse, if   [MP PET 1995]

    A)            \[r>2\]                                       

    B)            \[2<r<5\]

    C)            \[r>5\]                                       

    D)            None of these

    Correct Answer: B

    Solution :

               \[\frac{{{x}^{2}}}{2-r}+\frac{{{y}^{2}}}{r-5}+1=0\]Þ\[\frac{{{x}^{2}}}{r-2}+\frac{{{y}^{2}}}{5-r}=1\]            Hence \[r>2\]and \[r<5\]Þ\[2<r<5.\]


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