SOLUTION: find the center of the circle with these three points (3,5),(-3,11)and (-9,5)

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Question 330522: find the center of the circle with these three points (3,5),(-3,11)and (-9,5)
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
Use the equation of a circle centered at (h,k) with radius R.
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
Modify it slightly,
%28h-x%29%5E2%2B%28k-y%29%5E2=R%5E2
and generate equations using all three points.
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%28h-3%29%5E2%2B%28k-5%29%5E2=R%5E2
h%5E2-6h%2B9%2Bk%5E2-10k%2B25=R%5E2
1.h%5E2%2Bk%5E2-6h-10k%2B34=R%5E2
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%28h%2B3%29%5E2%2B%28k-11%29%5E2=R%5E2
h%5E2%2B6h%2B9%2Bk%5E2-22k%2B121=R%5E2
2.h%5E2%2Bk%5E2%2B6h-22k%2B130=R%5E2
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%28h%2B9%29%5E2%2B%28k-5%29%5E2=R%5E2
h%5E2%2B18h%2B81%2Bk%5E2-10k%2B25=R%5E2
3.h%5E2%2Bk%5E2%2B18h-10k%2B106=R%5E2
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Equate eq. 1 and eq. 2,
h%5E2%2Bk%5E2-6h-10k%2B34=h%5E2%2Bk%5E2%2B6h-22k%2B130
-6h-10k%2B34=6h-22k%2B130
-12h%2B12k=96
4.-h%2Bk=8
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Equate eq. 1 and eq. 3,
h%5E2%2Bk%5E2-6h-10k%2B34=h%5E2%2Bk%5E2%2B18h-10k%2B106
-6h-10k%2B34=18h-10k%2B106
-24h=72
h=-3
Then from eq. 4,
3%2Bk=8
k=5
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(-3,5)
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