From Förberedande kurs i matematik 1

If the circle is to contain the point (-1,1), then that point's distance away from the centre (2,-1) must equal the circle's radius, r. Thus, we can obtain the circle's radius by calculating the distance between (-1,1) and (2,-1) using the distance formula,

\displaystyle \begin{align} r &= \sqrt{(2-(-1))^2+(-1-1)^2} = \sqrt{3^2+(-2)^2} = \sqrt{9+4} = \sqrt{13}\,\textrm{.} \end{align}

When we know the circle's centre and its radius, we can write the equation of the circle,

\displaystyle (x-2)^2 + (y-(-1))^2 = (\sqrt{13})^{2}

which the same as

\displaystyle (x-2)^{2} + (y+1)^2 = 13\,\textrm{.}

Note: A circle having its centre at (a,b) and radius r has the equation

\displaystyle (x-a)^2 + (y-b)^2 = r^2\,\textrm{.}