How to tell the difference between hyperbolas parabolas and ellipses and circles?

Different difintions:
A circle is the set of all points in a plane that are equidistant from a given point called the centre of the circle.
An ellipse is the set of all poins in a plane such that sum of the distances from two fixed points (foci) is constant. 
A parabola the set of all points in a plane equidistant from a fixed point (focus) and a fixed line (directrix).
A hyperbola is the set of all points in a plane such that the difference of the distances from two fixed points (foci) is constant.

What the heck i didn’t know