Equidistance curves: equidistant points | Tangente

First steps ------------

The distance from a point M to a curve (C) is the smallest of the distances from M to a point m as it moves along (C). To say that M is equidistant from two curves (C₁) and (C₂) therefore means that Mm₁ = Mm₂, where m₁ and m₂ respectively attain the minimum distance from M to a point m on (C₁) or (C₂).

The distance from a point M to a circle (C) with center F and radius r is thus represented by the length MP, where P is the point on (C) "closest" to M. The points P, M, and F are collinear.

Point and circle ---------------

When A lies on (C), the locus of points equidistant from A and the circle (C), with center F, is the ray FA). Otherwise, two cases arise.