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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

user2097
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user265917
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  • In the first paragraph you are representing the curve as a graph $y=f(x)$ over the $x$ axis, and in the second paragraph, as an implicit level set $f(x,y) = 0$. Which are you interested in? (Spoiler alert: the answer won't be pleasant in any case.) – user7530 Sep 01 '15 at 01:16

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