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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

  • question_answer
    If the plane\[2ax-3at+4az+6=0\]passes through the midpoint of the line joining the centres of the spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\] and\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8,\]then a equals

    A)  \[-1\]             

    B)  1

    C)  \[-2\]             

    D)  2

    Correct Answer: C

    Solution :

     Centres of the first sphere is (-3, 4, 1) and the second sphere is (5, -2, 1). Their mid point is (1,1,1). Since it satisfies the equation of plane. So, \[2a-3a+4a+6=0\] \[\Rightarrow \] \[a=-2\]


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