Focus of a conic section

A conic section can be described as the locus of a point \(P\) whose distance \(PS\) from a fixed point \(S\) is in some fixed ratio \(e\) to its perpendicular distance \(PN\) from a fixed line.

The point \(S\) is called the focus of the conic, the fixed line is called the directrix of the conic, and the fixed ratio \(e\) is called the eccentricity of the conic.