VITEEE 2015 Paper

Given sphere is
x2+y2+z2 - 6x - 12y - 2z + 20 = 0
Centre = (3,6, 1)
Here, one end of diameter is (2, 7, 3).
Let the other end of the diameter be (x, y, z)
Centre of the sphere will be the mid-point of the ends of diameter.
So , (3 , 6 , 1) = (

2+x

2

,

7+y

2

,

3+z

2

)
⇒ 2 + x = 6 ⇒ x = 4
⇒ 7 + y = 12 ⇒ y = 5
and 3 + z = 2 ⇒ z= - 1
Therefore, (x, y, z) = (4, 5,-1)