I have a plane curve given by $y = f(x)$. At every point on this curve, I construct a normal direction to this curve and move the point a fixed distance $s$ along the normal to a new point. What is the equation of this new curve ?
For example, for a circle given by $x^2 + y^2 = 1$, the new curve is $x^2 + y^2 = (1+s)^2$.
Thanks