KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    C is the centre of ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\] and A and B are two points on the ellipse such that \[\angle ACB=90{}^\circ ,\] then is equal to

    A) \[\frac{25}{144}\]         

    B) \[\frac{144}{25}\]

    C) \[\frac{7}{12}\]                         

    D) \[\frac{12}{7}\]

    Correct Answer: A

    Solution :

    Equation of ellipse \[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1\]
    \[\angle ACB=90{}^\circ \]
    \[\Rightarrow \]\[\frac{1}{C{{A}^{2}}}+\frac{1}{C{{B}^{2}}}=\frac{1}{16}+\frac{1}{9}=\frac{25}{144}\]

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