2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Three Dimensional Geometry

JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Self Evaluation Test - Three Dimensional Geometry

  • question_answer
    If the plane \[2ax-3ay+4az+6=0\] 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 :

    [c] Plane \[2ax-3ay+4az+6=0\] passes through the midpoint of the centre of spheres \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+6x-8y-2z=13\] and \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-10x+4y-2z=8\] Respectively center of spheres are \[(-3,4,1)\] and \[(5,-2,1).\] Midpoint of centres is \[(1,1,1).\] Satisfying this in the equation of plane, we get \[2a-3a+4a+6=0\Rightarrow a=-2.\]


You need to login to perform this action.
You will be redirected in 3 sec spinner