The routine returns a list of two foci of the given ellipse or hyperbola f.

If the first optional argument fn is given, the names of the two foci are the two elements of the list fn.

See help pages for hyperbola and ellipse for definitions of the foci.

Use routine detail for more details on the foci.

The command with(geometry,foci) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{\_EnvHorizontalName}≔x\:$$\mathrm{\_EnvVerticalName}≔y\:$

$\mathrm{ellipse}\left(\mathrm{e1}\,2x^2+y^2-4x+4y=0\right)\:$

$\mathrm{foci}\left(\mathrm{e1}\right)$

$\left[\mathrm{foci\_1\_e1}\,\mathrm{foci\_2\_e1}\right]$

$\mathrm{map}\left(\mathrm{coordinates}\,\right)$

$\left[\left[1\,-2-\sqrt{3}\right]\,\left[1\,-2+\sqrt{3}\right]\right]$

$\mathrm{foci}\left(\left[\mathrm{f1}\,\mathrm{f2}\right]\,\mathrm{e1}\right)$

$\left[\mathrm{f1}\,\mathrm{f2}\right]$

$\mathrm{foci}\left(\mathrm{e1}\right)$

$\left[\mathrm{f1}\,\mathrm{f2}\right]$

$\mathrm{map}\left(\mathrm{coordinates}\,\right)$

$\left[\left[1\,-2-\sqrt{3}\right]\,\left[1\,-2+\sqrt{3}\right]\right]$