Definition:Ellipse/Equidistance

Definition

 * EllipseEquidistance.png

Let $F_1$ and $F_2$ be two points in the plane.

Let $d$ be a length greater than the distance between $F_1$ and $F_2$.

Let $K$ be the locus of points $P$ which are subject to the condition:
 * $d_1 + d_2 = d$

where:
 * $d_1$ is the distance from $P$ to $F_1$
 * $d_2$ is the distance from $P$ to $F_2$.

Then $K$ is an ellipse.

This property is known as the equidistance property.

The points $F_1$ and $F_2$ are the foci of $K$.

Also see

 * Equivalence of Definitions of Ellipse
 * Equidistance of Ellipse equals Major Axis