Definition:Hyperbola/Equidistance
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Definition
Let $F_1$ and $F_2$ be two points in the plane.
Let $d$ be a length less than the distance between $F_1$ and $F_2$.
Let $K$ be the locus of points $P$ which are subject to the condition:
- $\size {d_1 - d_2} = d$
where:
- $d_1$ is the distance from $P$ to $F_1$
- $d_2$ is the distance from $P$ to $F_2$
- $\size {d_1 - d_2}$ denotes the absolute value of $d_1 - d_2$.
Then $K$ is a hyperbola.
The points $F_1$ and $F_2$ are the foci of $K$.
Also see
Sources
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {IV}$. The Ellipse: $1 \text a$. Focal properties