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KVPY Sample Paper KVPY Stream-SX Model Paper-1

  • question_answer
    Suppose two perpendicular tangents can be drawn from the origin to the circle \[{{x}^{2}}+{{y}^{2}}-6x-2py+17=0,\] for some real p. Then,\[|p|\]is equal to

    A) 0                                 

    B) 3

    C) 5                                 

    D) 17

    Correct Answer: C

    Solution :

    [c]
    We have,
    \[{{x}^{2}}+{{y}^{2}}-6x-2py+17=0\]
    \[{{(x-3)}^{2}}+{{(y-p)}^{2}}=9-17+{{p}^{2}}\]
    Director circle of the given circle is
    \[{{(x-3)}^{2}}+{{(y-p)}^{2}}=2\,({{p}^{2}}-8)\]
    It is passes through (0, 0).
    \[\therefore \]\[9+{{p}^{2}}=2{{p}^{2}}-16\]
    \[\Rightarrow \]\[{{p}^{2}}=25\]
    \[\Rightarrow \]\[\left| p \right|=5\]


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