SOLUTION: make an equation for the circle that goes through the points (9,2) , (-1,12), and (-9,-4)

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Question 1167508: make an equation for the circle that goes through the points (9,2) , (-1,12), and (-9,-4)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of doing your problem for you, I'll do a different one that is EXACTLY
like yours step by step, that you can use as a guide for solving yours:

The one I'll solve is this one:
Find an equation for the circle that goes through the points (2,12) , (-7,3), and (11,3)


The general equation of the circle is:

x%5E2%2By%5E2%2BAx%2BBy%2BC=0

Substituting (x,y) = (2,12)

%282%29%5E2%2B%2812%29%5E2%2BA%282%29%2BB%2812%29%2BC=0

4%2B144%2B2A%2B12B%2BC=0

148%2B2A%2B12B%2BC=0

2A%2B12B%2BC=-148

Substituting (x,y) = (-7,3)

%28-7%29%5E2%2B%283%29%5E2%2BA%28-7%29%2BB%283%29%2BC=0

49%2B9-7A%2B3B%2BC=0

58-7A%2B3B%2BC=0

-7A%2B3B%2BC=-58

Substituting (x,y) = (11,3)

%2811%29%5E2%2B%283%29%5E2%2BA%2811%29%2BB%283%29%2BC=0

121%2B9%2B11A%2B3B%2BC=0

130%2B11A%2B3B%2BC=0

11A%2B3B%2BC=-130


The system to solve is this:

system%282A%2B12B%2BC=-148%2C-7A%2B3B%2BC=-58%2C11A%2B3B%2BC=-130%29

Subtract the first two equations:

   2A+12B+C=-148
-[-7A+ 3B+C= -58]


Change signs in bottom equation 

  2A+12B+C=-148
  7A- 3B-C=  58
---------------
  9A+ 9B  = -90

Subtract the first and third equations:

   2A+12B+C=-148
-[11A+ 3B+C=-130]

  2A+12B+C=-148
-11A- 3B-C= 130
----------------
 -9A+ 9B  = -18

Solve the system:

system%28++9A%2B+9B++=+-90%2C-9A%2B+9B++=+-18%29
        
Add them term by term

 9A+9B=-90
-9A+9B=-18
--------------
   18B=-108
     B=-6  

Substitute in

   9A+9B=-90
9A+9(-6)=-90
9A-54=-90
   9A=-36
    A=-4 

Substituting in

2A+12B+C=-148
2(-4)+12(-6)+C=-148
  -8-72+C=-148
    -80+C=-148
        C=-68

So the equation of the circle 

x%5E2%2By%5E2%2BAx%2BBy%2BC=0

becomes
x%5E2%2By%5E2-4x-6y-68=0


Now do yours the EXACT same way.

Edwin