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Question

If (2,3,5) is one end of a diameter of the sphere x2+y2+z26x12y2z+20=0 , then the coordinates of the other end of the diameter are

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

The correct option is B (4,9,3)
Equation of the sphere is : x2+y2+z26x12y2z+20=0

One end of the diameter is A(2,3,5)
Let us consider (x,y,z) be the other end of the diameter

Center C = mid point of AB..

[2+x2,3+y2,5+z2]=(3,6,1)

2+x2=3 2+x=6 x=4.

3+y2=6 3+y=12 y=9.

5+z2=1 5+z=2 z=3.

Other end of the diameter is B(4,9,3)

825457_163775_ans_75e782c537c84f298cfcb51c61f4b542.png

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