SOLUTION: find the equation of a circle passing through the points (-3,6),(-5,2),(3,-6)

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Question 1031604: find the equation of a circle passing through the points (-3,6),(-5,2),(3,-6)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The standard equation of a circle is

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

Substituting the three points we have this system:



Simplifying and rearranging the terms:



Subtracting the third equation from the first:

12h-24k=0
h-2k=0
h=2k

Subtracting the second equation from the first:

-4h-8k%2B16=0
h%2B2k-4=0

Substituting 2k for h

2k%2B2k-4=0
4k-4=0
4k=4
h=1

So the center = (h,k) = (2,1)

Substituting h=2 and k=1 in the first equation

h%5E2%2B6h%2Bk%5E2-12k%2B45=r%5E2
2%5E2%2B6%282%29%2B1%5E2-12%281%29%2B45=r%5E2
4%2B12%2B1-12%2B45=r%5E2
50=r%5E2
sqrt%2850%29=r
5sqrt%282%29=r

The equation

%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 becomes

%28x-2%29%5E2%2B%28y-1%29%5E2=50

Or if you multiply that out and get the general form:

x%5E2%2By%5E2-4x-2y%2B45=0


Edwin