Question

Find the centre of curvature of the astroid

x^2/3+y^2/3=a^2/3

Answer 1

L=2Pi*R

L=6a

R=L/2Pi

R=6a/2Pi=3a/Pi

Distance btw (0,0) and O-centre of curve is R: Ox=R and Oy=R

Centre of the circle O(3a/Pi, 3a/Pi)