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Manipal Engineering Manipal Engineering Solved Paper-2012

  • question_answer
    If P is a variable point on the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\] with\[AA\]as major axis. Then, the maximum value of the area of the\[\Delta \,\,APA\]is

    A) \[ab\,\,sq\,\,unit\]                         

    B) \[2\,\,ab\,\,sq\,\,unit\]

    C) \[\frac{ab}{2}sq\,\,unit\]             

    D)         None of these

    Correct Answer: A

    Solution :

    The maximum area corresponds to when\[P\]is at either end of the minor axis. \[\therefore \]Required area\[=\frac{1}{2}(2a)b=ab\]sq unit


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