Two conics are confocal if they have coincident foci.

Examples

1. 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. 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.