I need help with these 2 problems please and please make it legible.

Find an equation for the circle of curvature of the curve r(t) = 3t i + sin(5t) j at the point 2.1 . (The curve parameterizes the graph of y = sin ex in the xy -plane . ) Choose the correct equation for the circle of curvature. . . . . O A. x - 2 +y - _ 16) 2 81 =. 25 625 O B. 37 ) 2 x - 625 2 + ( y - 1) 2 = 81 O c. x - _ 3TC ) 2 2 + (y - 1) 2 = 81 625 O D. + y - 34 ) 2 625 25 =. 81Write a in the form a = aTT + aNN at the given value of t without finding T and N. r(t) = (212) i+ 21 + 2+3 )1+ 21- 2+3 ) k, 1 = 1 . . . . . a(1) = ()T + (N (Type exact answers, using radicals as needed.)