well, yes, its center is at (-1 , 1), now, we have a nice blue point on the IV Quadrant, namely at (6 , -4), so we know the circle passes through (6 , -4), let's check for that distance from the center to that blue point.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})}\qquad \stackrel{blue~point}{(\stackrel{x_2}{6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~6 - (-1)~~)^2 + (~~-4 - 1~~)^2} \implies d=\sqrt{(6 +1)^2 + (-4 -1)^2} \\\\\\ d=\sqrt{( 7 )^2 + ( -5 )^2} \implies d=\sqrt{ 49 + 25 } \implies d=\sqrt{ 74 } \\\\[-0.35em] ~\dotfill[/tex]
[tex](x + 1)^2~~ + ~~(y-1)^2~~ = ~~(\sqrt{74})^2\implies (x + 1)^2~~ + ~~(y-1)^2~~ = ~~74[/tex]
