Chapter 10.4, Problem 7AYU

A(n) _______ is the collection of points in a plane the difference of whose distances from two fixed points is a constant.

To determine

To find: What is the collection of all points in a plane the difference of whose distances from two fixed points is a constant.

Answer to Problem 7AYU

Solution:

Hyperbola.

Explanation of Solution

Given:

The collection of all points in a plane the difference of whose distances from two fixed points is a constant.

Calculation:

An hyperbola is the collection of all points in a plane, the difference of whose distances from two fixed points, called the foci, is a constant.

The point $F_1$ and $F_2$ is called the foci, the line containing foci is called transverse axis. The midpoint of the line segment joining the foci is the center of the ellipse. The line through the center and perpendicular to the transverse axis is the conjugate axis.