| http://www.w3.org/ns/prov#value | - An equivalent condition to P2 being at the furthest point in the m-P2 direction from P1-P3 on the ellipse is for the tangent line to P2 to be parallel to the line P1-P3; this is essentially the idea behind Lagrange multipliers; the key is that the normal vector, i.e. the gradient of the defining equation determining level sets, is then perpendicular to the line P1-P3.
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