Question

find the radius and center of curvature of the parabola y=x^2 -4x + 4 at any point (x,y) on the curve.draw the circle of curature.

Answer 1

y' = 2x-4
y" = 2

radius: |(1+y'^2)^(3/2)/y"|
= |(1+(2x-4)^2)^(3/2))/2
= |(4x^2-16x+17)^(3/2)/2|

curvature = 1/radius

There is no general circle to draw. You need to specify a point.