Find the minimum distance between a point in the plane and a quadratic Plane Curve
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
Minimizing the distance therefore requires solution of a Cubic Equation.
See also Point-Point Distance--1-D, Point-Point Distance--2-D,
© 1996-9 Eric W. Weisstein