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AP EAMCET2010MathematicsThree Dimensional Geometry

If (2,3,-3) is one end of a diameter of the sphere x^2+y^2+z^2-6 x-12 y-2 z+20=0 , then the other end of the diameter is

Options

  1. A(4,9,-1)
  2. B(4,9,5)
  3. C(-8,-15,1)
  4. D(8,15,5)

Correct answer

B. (4,9,5)

Step-by-step solution

The equation of the sphere is x^2+y^2+z^2-6 x-12 y-2 z+20=0 So, the centre of the sphere is (-u,-v,-w)=(3,6,1) given the one end of the diameter is (2,3,-3) , let the other end of the diameter is ( , , ) . Since, O is the mid point of the diameter, then (3,6,1)= [ +2 2 , +3 2 , -3 2 ] +2 2 =3, =4 +3 2 =6, =9 -3 2 =1, =5 Hence, the other end is (4,9,5) .

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