Answer
$$r = 5$$
Work Step by Step
$$\eqalign{
& {x^2} + {y^2} = 25 \cr
& {\text{Convert to polar form, using }}x = r\cos \theta ,{\text{ }}y = r\sin \theta \cr
& {\left( {r\cos \theta } \right)^2} + {\left( {r\sin \theta } \right)^2} = 25 \cr
& {r^2}{\cos ^2}\theta + {r^2}{\sin ^2}\theta = 25 \cr
& {r^2}\left( {{{\cos }^2}\theta + {{\sin }^2}\theta } \right) = 25 \cr
& {r^2}\left( 1 \right) = 25 \cr
& r = 5 \cr
& {\text{The equation represents a circle of radius 5 centered at the origin}} \cr
& {\text{Graph}} \cr} $$
