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10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

  • question_answer
    If the points \[A(4,3)\] and \[B(x,5)\] are on the circle with centre \[O(2,3),\] then the value of k is:

    A) 5

    B) 6

    C) 2

    D) 4

    Correct Answer: C

    Solution :

    [c] Since A and B lie on the circle having centre O.
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,OA=OB\] (Each equal to radius]
    \[\Rightarrow \,\,\,\,\sqrt{{{(4-2)}^{2}}+{{(3-3)}^{2}}}=\sqrt{{{(x-2)}^{2}}+{{(5-3)}^{2}}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2=\sqrt{{{(x-2)}^{2}}+4}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4={{(x-2)}^{2}}+4\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{(x-2)}^{2}}=0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x-2=0\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=2\]


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