184. Write the equations of the circles: 1) with center at point $C(-2 ; 3)$ and radius $R=5$; 2) with center at point $C\left(\frac{1}{3} ;-1\right)$ and radius $R=\frac{1}{2}$.
Solution. 1) Given $a=-2, b=3, R=5$, therefore, by formula (3) we obtain the required equation of the circle

$$
(x+2)^{2}+(y-3)^{2}=25
$$

or

$$
x^{2}+4 x+4+y^{2}-6 y+9=25
$$

or

$$
x^{2}+y^{2}+4 x-6 y-12=0
$$

2) Here $a=\frac{1}{3}, b=-1, R=\frac{1}{2}$, therefore, the equation of the circle will be:

or

$$
\begin{gathered}
\left(x-\frac{1}{3}\right)^{2}+(y+1)^{2}=\frac{1}{4} \\
36 x^{2}+36 y^{2}-24 x+72 y+31=0
\end{gathered}
$$