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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        The   greatest  distance  of  the   point\[P(10,7)\]from the circle\[{{x}^{2}}+{{y}^{2}}-4x-2y-20=0\]is:

    A)  \[10\]                                                  

    B)  15

    C)  5                                            

    D)  none of these

    Correct Answer: B

    Solution :

                    Since\[{{S}_{1}}={{10}^{2}}+{{7}^{2}}-4\times 10-2\times 7-20>0\]So, P lies outside the circle. Join P with the centre C(2, 1) of the given circle. Suppose PC cuts the circle at A and B then, PB is the greatest distance of P from the circle \[PC=\sqrt{{{(10-2)}^{2}}+{{(7-1)}^{2}}}\] \[=10\] \[BC=\sqrt{4+1+20}\] \[=5\] \[PB=PC+CB\] \[=10+5\] \[=15\]


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