Find the minimum distance between a point in the plane and a quadratic Plane Curve
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(1) |
The square of the distance is
Minimizing the distance squared is the equivalent to minimizing the distance (since and have minima at the
same point), so take
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(3) |
|
(4) |
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(5) |
Minimizing the distance therefore requires solution of a Cubic Equation.
See also Point-Point Distance--1-D, Point-Point Distance--2-D,
Point-Point Distance--3-D
© 1996-9 Eric W. Weisstein
1999-05-25