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.