y2 = 4ax
dy/dx = 2a/y
At (at2, 2at), dy/dx = 2a/2at = 1/t
d2y/dx2 = -2a/y2 x dy/dx
At at2, 2at
d2y/dx2 = -2a/(4a2t2) x 1/t = -1/(2at3)
Radius of curvature R at at2, 2at
= (1+(dy/dx)2)3/2/ (d2y/dx2)
= (1+1/t2)3/2/(1/(2at3))
(Negative sign may be removed)
= 2at3(t2+1)3/2/ t3
= 2a(t2+1)3/2