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Possible Duplicate:
Calculating Distance of a Point from an Ellipse Border

Given a point $A = (x_1, y_1)$ and a $2$D ellipse, how could we find a point $B = (x_2, y_2)$ on the ellipse so that it has the shortest distance between point $A$ and $B$?

The point $A$ can be anywhere on the same plane of the ellipse. If possible, please list the final expression of the point $B.$

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    What have you already attempted? Hints: 1. What is the distance between two points? 2. If your point $(x_2,y_2)$ is on the ellipse, what must be true about it (e.g. It must satisfy the equation for the ellipse).2012-08-22
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    I believe my answer in the follow post maybe helpful. http://math.stackexchange.com/questions/90974/calculating-distance-of-a-point-from-an-ellipse-border/90984#909842012-08-23
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    @Jin: You have not told us what are the given data about the ellipse, e.g., whether its axes are parallel to the coordinate axes or not. Maybe the ellipse is given by $5$ of its points; then the solution of your problem looks very unintuitive.2012-10-22

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