The distance from a point to a curve is found by minimizing the distance between the point and a generic point on the curve. A further analysis to this solution can be found in this related MaplePrimes blog post by Dr. Lopez.
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3-8_MinimizationProblem.mw
3-8_MinimizationProblem.zip
Newton's Method Tutor Newton's Method Differentiation
Watch the recorded webinar Read the blog post