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10th Class Mathematics Coordinate Geometry Question Bank Co-ordinate Geometry

  • question_answer
    If points A (2, 0) and B (8, -4) are the end points of diameter AB of circle 0, then area of circle 0 is

    A)  \[10\,\pi \]                        

    B)         \[13\,\pi \]  

    C)  \[24\,\pi \]                                        

    D)  \[26\,\pi \]

    Correct Answer: B

    Solution :

     Here, the points \[A\,(2,0)\] and \[B\,(8,-4)\] are the end points of diameter AB. So, by distance formula Diameter, \[AB=\sqrt{{{(-4-0)}^{2}}+{{(8-2)}^{2}}}\]                 \[=\sqrt{16+36}=\sqrt{52}\]                 \[=\sqrt{4\times 13}=2\sqrt{13}\] \[\therefore \] Radius \[=\frac{2\sqrt{13}}{2}=\sqrt{13}\] Now, area of the circle \[=\pi \] (radius)2                 \[=\pi (\sqrt{13})2=13\pi \]


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