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Question

If (2, 3, 5) is one end of a diameter of the sphere x2+y2+z2−6x−12y−2z+20=0, then the coordinates of the other end of the diameter are-

A
(4, 9, -3)
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B
(4, -3, 3)
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C
(4, 3, 5)
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D
(4, 3, -3)
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Solution

The correct option is D (4, 9, -3)
Let other end be (a,b,c)
Using diameter form, we get
(x2)(xa)+(y3)(yb)+(z5)(zc)=x2+z2+y26x12y2z+20
On comparing, we get
2+a=6a=4
3+b=12b=9
5+c=2c=3
So, other end will be (4,9,3)

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