<s>[INST] Find the equation of the circle passing ... Find the equation of the circle passing through the points $P(5,7)$, $Q(6,6)$ and $R(2,-2)$.
My Attempt:
Let the equation of the circle be:
$$x^2+y^2+2gx+2fy+c=0$$
The point $P(5,7)$ lies on the circle then,
$$5^2+7^2+10g+14f+c=0$$
$$10g+14f+c=-74$$-----(1)
The point $Q(6,6)$ lies on the circle then,
$$6^2+6^2+12g+12f+c=0$$
$$12g+12f+c=-72$$-------(2)
The point $R(2,-2)$ lies on the circle the,
$$2^2+(-2)^2+4g-4f+c=0$$
$$4g-4f+c=0$$-----(3).
Now, please help me from here.
 [/INST] $\begin{vmatrix}
x^2+y^2&x&y&1\\
5^2+7^2&5&7&1\\
6^2+6^2&6&6&1\\
2^2+(-2)^2&2&-2&1
\end{vmatrix}=0$    
$-12(x^2+y^2)+48x+72y+144=0$
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