focus

The parabola is a plane curve defined as the set of all points that are equidistant from a fixed point \(F \) called the focus, and a fixed line \( d \) called the directrix.

Given two fixed points in the plane, \( F_1 \) and \( F_2 \), a hyperbola is defined as the set of all points \( P \) such that the absolute value of the difference between the distances from \( P \) to each focus is constant.