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Topic: Shortest Distance to Ellipse from Point?
Replies: 4   Last Post: Jul 26, 2010 3:38 PM

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Alexander Bogomolny

Posts: 406
Registered: 12/4/04
Re: Shortest Distance to Ellipse from Point?
Posted: Apr 9, 2010 8:18 PM
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A good idea is to check Joachimsthal's Notations: http://www.cut-the-knot.org/Generalization/JoachimsthalsNotations.shtml. With this, you immediately get an equation of a tangent to ellipse and then also that of a normal.

You need to find a point on the ellipse, meaning there are two unknowns. You'll have to have two equations. You get one by substituting the given point into the normal. The equation of the ellipse is the other. The two reduce to a quadratic equation in one of the unknown coordinates.



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