<s>[INST] Find the equation of a circle containing three given points Problem:

Determine the equation of the circle that passes through three points, $J(-3, 2)$, $K(4, 1)$, and $L(6, 5)$.

I thought of using systems like so:
$$\left\{ \begin{array}{rcl} (x+3)^2 + (y-2)^2 = r^2 \\ (x-4)^2 + (y-1)^2 = r^2 \\ (x-6)^2 + (y-5)^2 = r^2 \\ \end{array} \right.$$ 
After equating the expressions on the left hand side of each equation, expanding and simplifying, I found out that $y = 7x -2$. I decided to substitute the $y$ into two of the expressions to solve for $x$. But it only gives me $50x^2 - 50x + 25 = 50x^2 - 50x + 25$, which does not help. Can someone please help me out? Thanks!
 [/INST] Use the equation $x^2+y^2+2gx+2fy+c=0$. Substitute those values, you will get three equations involving g,f,c. Substituting the values back to the equation will be your equation. The answer will be $x^2+y^2-2x-10y+1=0$ or $(x-1)^2+(y-5)^2=25$
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