confocal
Two conics are confocal if they have coincident foci.
Examples

1.
The family of ellipses
$$\frac{{x}^{2}}{{a}^{2}+s}+\frac{{y}^{2}}{{b}^{2}+s}=1,$$ where ${a}^{2}>{b}^{2}$ and the parameter $s$ is $>{b}^{2}$, is confocal.

2.
The family of hyperbolas
$$\frac{{x}^{2}}{{a}^{2}t}\frac{{y}^{2}}{t{b}^{2}}=1,$$ where ${a}^{2}>{b}^{2}$ and the parameter $t$ is between ${a}^{2}$ and ${b}^{2}$, is confocal.
Title  confocal 

Canonical name  Confocal 
Date of creation  20130322 14:44:58 
Last modified on  20130322 14:44:58 
Owner  Mathprof (13753) 
Last modified by  Mathprof (13753) 
Numerical id  6 
Author  Mathprof (13753) 
Entry type  Definition 
Classification  msc 51N20 