recall that the distance from the center of a circle to a point on the circle is the radius. Therefore, the distance between (5, -4) and (-3, 2) is "r".
[tex] \bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4})\qquad
(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2})\qquad \qquad
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
\stackrel{radius}{r}=\sqrt{[-3-5]^2+[2-(-4)]^2}\implies r=\sqrt{(-3-5)^2+(2+4)^2}
\\\\\\
r=\sqrt{(-8)^2+6^2}\implies r=\sqrt{100}\implies r=10\\\\
------------------------------- [/tex]
[tex] \bf \textit{equation of a circle}\\\\
(x- h)^2+(y- k)^2= r^2
\qquad
center~~(\stackrel{5}{ h},\stackrel{-4}{ k})\qquad \qquad
radius=\stackrel{10}{ r}
\\\\\\\
[x-5]^2+[y-(-4)]^2=10^2\implies (x-5)^2+(y+4)^2=100 [/tex]
