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.

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