(Solved): Find an equation for the circle of curvature of the curve \( r(t)=2 t i+\sin (5 t) j \) at the poi ...

Find an equation for the circle of curvature of the curve \( r(t)=2 t i+\sin (5 t) j \) at the point \( (\pi, 1) \). (The curve parameterizes the graph of \( y=\sin \left(\frac{5}{2} x\right) \) in the \( x y- \) plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using \( \pi \) as needed.)