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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

  • question_answer
    If the length of the major axis of the ellipse\[\left( \frac{{{x}^{2}}}{{{a}^{2}}} \right)+\left( \frac{{{y}^{2}}}{{{b}^{2}}} \right)=1\]is three times the length of minor axis, its eccentricity is:

    A)  \[\frac{1}{3}\]                  

    B)         \[\frac{1}{\sqrt{3}}\]                    

    C)  \[\sqrt{\frac{2}{3}}\]                    

    D)         \[\frac{2\sqrt{2}}{3}\]

    E)  none of these

    Correct Answer: D

    Solution :

    Length of minor axis\[=2b\] and According to the given condition length of major axis\[=3(2b)=6b\] \[\therefore \]  \[e=\sqrt{1-\frac{{{b}^{2}}}{{{(3b)}^{2}}}}=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}\]


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