Respuesta :
the distance from the center of a circle to a point on the circle goes by the name of radius, so the distance between these two points is just that.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[6-3]^2+[2-(-1)]^2}\implies r=\sqrt{(6-3)^2+(2+1)^2} \\\\\\ r=\sqrt{3^2+3^2}\implies r=\sqrt{18} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{\sqrt{18}}{ r}\\[2em] [x-3]^2+[y-(-1)]^2=(\sqrt{18})^2\implies (x-3)^2+(y+1)^2=18[/tex]
