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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

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

    A)  \[\lambda >5\]                                

    B)  \[\lambda <2\]

    C)  \[2<\lambda <5\]                           

    D)  \[2>\lambda >5\]

    Correct Answer: B

    Solution :

    Given equation can be rewritten as \[\frac{{{x}^{2}}}{2-\lambda }+\frac{{{y}^{2}}}{-\lambda +5}=1\] To represents an ellipse,                 \[2-\lambda >0\] and \[-\lambda +5>0\]                 \[\lambda <2\] and \[\lambda <5\] \[\therefore \]  \[\lambda <2\]


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