\[
(x-0)(x-2)+(y-0)(y-3)=0
\]
or
\[
x^{2}+y^{2}-2 x-3 y=0
\]
(c) Three Point Form
If three non-collinear points are given, then through them passes a unique circle. In fact, the points are \( \left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right) \) and \( \left(x_{3}, y_{3}\right) \) then the equation of the circle will be
\[
\left|\begin{array}{llll}
x^{2}+y^{2} & x & y & 1 \\
x_{1}^{2}+y_{1}^{2} & x_{1} & y_{1} & 1 \\
x_{2}^{2}+y_{2}^{2} & x_{2} & y_{2} & 1 \\
x_{3}^{2}+y_{3}^{2} & x_{3} & y_{3} & 1
\end{array}\right|=0
\]
To see this: suppose that the equation of the circle
\[
x^{2}+y^{2}+2 g x+2 f+c=0
\]