SOLUTION: Find the equation of the sphere with diameter endpoints (2, -7, -2) and (-4, 3, 2).

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Question 1136326: Find the equation of the sphere with diameter endpoints (2, -7, -2) and (-4, 3, 2).
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the sphere with diameter endpoints (2,-7,-2) and (-4,3,2).
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d^2 = diffx^2 + diffy^2 + diffz^2 = 36 + 100 + 16 = 152
r^2 = d^2/4 = 38
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The center is ((2-4)/2,(-7+3)/2,(-2-2)/2) --- (x,y,z)
--> (-1,-2,0)
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%28x%2B1%29%5E2+%2B+%28y%2B2%29%5E2+%2B+z%5E2+=+38

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The diameter length is


sqrt%28+%28%28-4%29-2%29%5E2++%2B+%283-%28-7%29%29%5E2+%2B+%282-%28-2%29%29%5E2%29 = sqrt%2836+%2B+100+%2B+16%29 = sqrt%28152%29.


The center is  (%282+%2B+%28-4%29%29%2F2, %28%28-7%29%2B3%29%2F2,%28%28-2%29%2B2%29%2F2) = (-1,-2,0).


Therefore, the equation of the sphere is


%28x-%28-1%29%29%5E2 + %28y-%28-2%29%29%5E2 + z%5E2 = %28sqrt%28152%29%2F2%29%5E2,   or, equivalently,


%28x%2B1%29%5E2 + y%2B2%29%5E2 + z%5E2 = 152%2F4,   which is


%28x%2B1%29%5E2 + y%2B2%29%5E2 + z%5E2 = 38.    ANSWER

Solved.