Circle: The locus of points in a plane whose distance from a specified point is the same. The fixed point is called the center

Ellipse: The locus of points the sum of whose distance from two fixed points is constant. The two fixed points are called foci.

Hyperbola: The locus of two points is the difference of whose distance from two fixed points is constant. The two fixed points are called foci.

Parabola: The locus of points in a plane such that each point is the same difference from a line (called the directrix) and a fixed point (called the focus)