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KVPY Sample Paper KVPY Stream-SX Model Paper-10

  • question_answer
    An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is 2/3 then the eccentricity of the ellipse is:

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

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

    C) \[\frac{8}{9}\]                          

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

    Correct Answer: A

    Solution :

    \[\frac{2}{3}=\frac{\pi {{a}^{2}}-\pi ab}{\pi {{a}^{2}}}=1-\frac{b}{a}=1-\sqrt{1-{{e}^{2}}}\] \[\Rightarrow \]\[{{e}^{2}}=\frac{8}{9}\]\[\Rightarrow \]\[e=\frac{2\sqrt{2}}{3}\]


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