SOLUTION: find the equation of circle through the points (10,2),(2,3),(1,-1)

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Question 1097128: find the equation of circle through the points (10,2),(2,3),(1,-1)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general form of the circle,
x%5E2%2By%5E2%2BAx%2BBy%2BC=0
.
.
(10,2):
10%5E2%2B2%5E2%2B10A%2B2B%2BC=0
1.10A%2B2B%2BC=-104
.
.
(2,3):
2%5E2%2B3%5E2%2B2A%2B3B%2BC=0
2.2A%2B3B%2BC=-13
.
.
(1,-1):
1%5E2%2B%28-1%29%5E2%2BA-B%2BC=0
3.A-B%2BC=-2
.
.
Subtract eq. 3 from eq. 1,
10A%2B2B%2BC-A%2BB-C=-104%2B2
9A%2B3B=-102
4.3A%2BB=-34
Subtract eq. 3 from eq. 2,
2A%2B3B%2BC-A%2BB-C=-13%2B2
5.A%2B4B=-11
Multiply eq. 3 by -4 and add to eq. 5,
-12A-4B%2BA%2B4B=136-11
-11A=125
A=-125%2F11
So then working backwards,
3A%2BB=-34
3%28-125%2F11%29%2BB=-34
B=-34%2B375%2F11
B=-374%2F11%2B375%2F11
B=1%2F11
and
A-B%2BC=-2
-125%2F11-1%2F11%2BC=-22%2F11
C=104%2F11
So then,
x%5E2%2By%5E2-%28125%2F11%29x%2B%281%2F11%29y%2B%28104%2F11%29=0
Complete the square in both x and y,




%28x-125%2F22%29%5E2%2B%28y%2B1%2F22%29%5E2%2B%28104%2F11%29=11050%2F484
highlight%28%28x-125%2F22%29%5E2%2B%28y%2B1%2F22%29%5E2%2B%28104%2F11%29=5525%2F242%29