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JEE Main & Advanced AIEEE Solved Paper-2008

  • question_answer
    A focus of an ellipse is at the origin. The directrix is the line \[x=4\] and the eccentricity is \[\frac{1}{2}\]. Then the length of the semimajor axis is       AIEEE  Solved  Paper-2007

    A) \[\frac{4}{3}\]                   

    B)        \[\frac{5}{3}\]                   

    C)        \[\frac{8}{3}\]   

    D)        \[\frac{2}{3}\]

    Correct Answer: C

    Solution :

                                    Perpendicular distance from focus on directrix\[=\frac{\left| 0-4 \right|}{\sqrt{1}}=\frac{a}{e}-ae\Rightarrow 4=2a-\frac{a}{2}\]\[\Rightarrow 4=\frac{3a}{2}\Rightarrow a=\frac{8}{3}\]


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