It's very interesting that the parallel curve of parabola is not parabola..you can draw a parabola on your paper and use pen to go on by the line; you will see the parallel of the parabola will cross itself, so that's true the parallel of the parabola is not parabola; It's same to circle and sin curve;
Here is a useful formula to calculate the parallel curve and curvature and the radius of the curvature:
![X[x,y]=x+\frac{ay'}{\sqrt {x'^2+y'^2}}](http://upload.wikimedia.org/math/6/4/7/647b764f6b1bdc007709689a57500cc5.png)
![Y[x,y]=y-\frac{ax'}{\sqrt {x'^2+y'^2}}](http://upload.wikimedia.org/math/c/c/a/cca4c29ec2ebd10ce3636ad0cee4e1be.png)
Here y=f(t);x=g(t); X and Y are coordinate of the parallel curve.
See more:
http://en.wikipedia.org/wiki/Parallel_curvehttp://www.jstor.org/stable/3027202?seq=5
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